Method and apparatus for signal denoising

Abstract

The application provides a signal denoising method and device, the method comprising: performing multi-layer empirical mode decomposition on a baseband signal y(n) obtained by down-converting an LFM modulated pulse signal S(n), to obtain a plurality of intrinsic mode functions; reconstructing a signal component s(n) and a noise component N(n) of the baseband signal y(n) based on the intrinsic mode functions and energy values of the intrinsic mode functions; and determining a corresponding denoised signal based on amplitudes of discrete Fourier spectra of the reconstructed signal component s(n) and amplitudes of discrete Fourier spectra of the reconstructed noise component N(n). The application reconstructs signal components and noise components through intrinsic modes, and uses spectral amplitudes of noise intrinsic mode functions in empirical mode decomposition as thresholds for signal Fourier denoising, thereby achieving adaptive threshold denoising, and effectively achieving adaptive threshold denoising on an LFM pulse signal superimposed with additive stationary noise at a low signal-to-noise ratio.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar communication, and in particular to a signal denoising method and device. BACKGROUND

[0002] In the modern military field, radar signal recognition is an important prerequisite for ensuring that radar countermeasure detection and interference equipment effectively play their combat effectiveness. However, with the development of electronic technology, the electromagnetic environment is becoming increasingly complex, which puts forward higher requirements for radar signal recognition. In order to more effectively improve the accuracy of radar signal recognition, it is generally necessary to perform denoising processing on the received radar signal.

[0003] However, the common radar LFM signal is not a linear stationary signal, and cannot be denoised by traditional Fourier transform; wavelet decomposition denoising needs to manually select a wavelet basis function and a threshold function, and different basis functions and threshold functions can result in a large difference in denoising effect. The public traditional empirical mode decomposition denoising algorithm estimates the demarcation point of the low-frequency signal component and the high-frequency noise component of the intrinsic mode function, and realizes denoising by directly removing the high-frequency noise component. However, because the radar LFM signal is a linear frequency modulation signal, it belongs to a wideband signal, and the frequency is changing, the above method can better remove the high-frequency noise, but the low-frequency signal component often retains a part of the high-frequency noise component, and since only the high-frequency noise intrinsic mode function is discarded, the noise of the low-frequency signal cannot be effectively removed. Therefore, it is difficult to accurately remove the high-frequency and low-frequency noise at the same time in the process of removing the noise. If high and low frequency operations are performed together, the useful signal in the high frequency will be removed while removing the low frequency noise, and vice versa.

[0004] In order to further remove the low-frequency noise and improve the signal-to-noise ratio, some scholars have proposed applying wavelet decomposition to the signal denoised by empirical mode decomposition to realize further denoising, which can effectively remove some high-frequency noise residues and noise in the low-frequency signal. However, the selection of the wavelet basis function and the threshold function in wavelet decomposition denoising will have a greater impact on the result. SUMMARY

[0005] In view of the problems existing in the prior art, the present application provides a signal denoising method and device.

[0006] In a first aspect, the present application provides a signal denoising method, comprising:

[0007] The baseband signal y(n) obtained by down-converting the LFM modulated pulse signal S(n) is subjected to multi-layer empirical mode decomposition to obtain a plurality of intrinsic mode functions;

[0008] reconstructing a signal component s(n) and a noise component N(n) of the baseband signal y(n) based on the eigenmode function and an energy value of the eigenmode function;

[0009] determining a corresponding denoised signal z(n) based on an amplitude of a discrete Fourier spectrum of the reconstructed signal component s(n) and an amplitude of a discrete Fourier spectrum of the reconstructed noise component N(n).

[0010] Optionally, the baseband signal y(n) obtained by down-converting the LFM modulated pulse signal S(n) is subjected to multi-layer empirical mode decomposition to obtain a plurality of eigenmode functions, including:

[0011] determining, based on a spline difference function, an upper envelope e max (n) corresponding to all the maximum values y max (n) of the baseband signal y(n), and a lower envelope e min (n) corresponding to all the minimum values y min (n) of the baseband signal y(n);

[0012] determining a high-frequency detail signal d(n) based on a difference between the baseband signal y(n) and an average value m(n) of the upper and lower envelopes;

[0013] if it is determined that the high-frequency detail signal d(n) satisfies an eigenmode function condition, determining that the high-frequency detail signal d(n) is an eigenmode function IMF i (n) obtained by the multi-layer empirical mode decomposition;

[0014] determining a corresponding residual signal r(n) based on a difference between the baseband signal y(n) and the eigenmode function IMF i (n);

[0015] if it is determined that the residual signal r(n) satisfies an end condition of the multi-layer empirical mode decomposition, determining that all the eigenmode functions IMF i (n) constitute the plurality of eigenmode functions.

[0016] Optionally, the method further includes:

[0017] if it is determined that the high-frequency detail signal d(n) does not satisfy the eigenmode function condition, updating the baseband signal y(n) with the high-frequency detail signal d(n);

[0018] determining a new high-frequency detail signal d(n) based on the updated baseband signal y(n).

[0019] Optionally, the method further includes:

[0020] if it is determined that the residual signal r(n) does not satisfy the end condition of the multi-layer empirical mode decomposition, updating the baseband signal y(n) with the residual signal r(n);

[0021] based on the updated residual signal r(n), determining a new residual signal r(n).

[0022] Optionally, the reconstructing the signal component s(n) and the noise component N(n) of the baseband signal y(n) based on the intrinsic mode function and the energy value of the intrinsic mode function comprises:

[0023] determining the energy value corresponding to each intrinsic mode function, and constructing an energy spectrum corresponding to all intrinsic mode functions;

[0024] determining the serial number of the intrinsic mode function corresponding to the point of energy mutation in the energy spectrum, and taking the serial number as a boundary point;

[0025] determining the noise component N(n) of the reconstructed baseband signal y(n) based on the sum of all intrinsic mode functions with serial numbers less than the boundary point;

[0026] determining the signal component s(n) of the reconstructed baseband signal y(n) based on the sum of all intrinsic mode functions with serial numbers greater than or equal to the boundary point and the residual signal.

[0027] Optionally, the determining the denoised signal z(n) based on the amplitude of the discrete Fourier spectrum of the reconstructed signal component s(n) and the amplitude of the discrete Fourier spectrum of the reconstructed noise component N(n) comprises:

[0028] determining the discrete Fourier spectrum of the reconstructed signal component s(n) and the discrete Fourier spectrum of the reconstructed noise component N(n) based on the discrete Fourier transform, respectively;

[0029] determining the amplitude of the denoised signal z(n) based on the size of the amplitude of the discrete Fourier spectrum of the signal component s(n) and the amplitude of the discrete Fourier spectrum of the noise component N(n);

[0030] performing inverse discrete Fourier transform on the amplitude of the denoised signal z(n) to determine the denoised signal z(n).

[0031] Optionally, the determining the amplitude of the denoised signal z(n) based on the size of the amplitude of the discrete Fourier spectrum of the signal component s(n) and the amplitude of the discrete Fourier spectrum of the noise component N(n) comprises:

[0032] If the amplitude of the discrete Fourier spectrum of the signal component s(n) is greater than the amplitude of the discrete Fourier spectrum of the noise component N(n), then the difference between the two amplitudes is determined as the amplitude of the denoised signal z(n);

[0033] If the amplitude of the discrete Fourier spectrum of the signal component s(n) is less than or equal to the amplitude of the discrete Fourier spectrum of the noise component N(n), then the amplitude of the denoised signal z(n) is determined as zero.

[0034] Optionally, the amplitude of the denoised signal z(n) is subjected to inverse discrete Fourier transform to determine the denoised signal z(n), and the specific formula is:

[0035]

[0036] wherein Z(n) is the amplitude of the denoised signal z(n), N is the sequence length of z(n), n is the sequence number of the sequence z(n), k is the signal frequency domain component, F -1 [] is the inverse discrete Fourier transform.

[0037] Optionally, the intrinsic mode function satisfies the following conditions:

[0038] In the entire time range corresponding to the LFM modulated pulse signal S(n), the number of all maximum values y max (n) and the number of all minimum values y min (n) are equal to or differ by one from the number of zero-crossing points of the baseband signal y(n).

[0039] And in any time period, the average value m(n) of the upper and lower envelopes is zero.

[0040] Optionally, the end condition of the multi-layer empirical mode decomposition is that the residual signal is a monotonic function or the maximum value of the residual signal r(n) is less than a specified threshold SD, and the specified threshold SD and the intrinsic mode function IMF i (n) are in one-to-one correspondence.

[0041] Optionally, the specified threshold SD and the intrinsic mode function IMF i (n) are in one-to-one correspondence, and the specific correspondence relationship is:

[0042]

[0043] wherein h i (t) is the Hilbert transform of the intrinsic mode function IMF i (n), the range 0-T is the length of the entire intrinsic mode function IMF i (n), and i is the intrinsic mode function IMF ithe sequence number of (n).

[0044] Optionally, the LFM modulated pulse signal S(n) is received by the receiver at a sampling rate f s a discrete signal obtained by receiving a radio frequency signal S(t), wherein the sampling rate f s is greater than the Nyquist sampling rate.

[0045] Optionally, the spline difference function is a cubic spline difference.

[0046] Optionally, the average value m(n) of the upper and lower envelopes is determined by a predefined formula, and the predefined formula is:

[0047]

[0048] wherein e max (n) is all the maximum values y max (n) corresponds to the upper envelope, e min (n) is all the minimum values y min (n) corresponds to the lower envelope.

[0049] Optionally, the energy value corresponding to each intrinsic mode function is determined, and an energy spectrum corresponding to all intrinsic mode functions is constructed, including:

[0050] According to the energy formula, the energy value of each intrinsic mode function is determined to form a corresponding energy spectrum; and the energy formula is:

[0051]

[0052] wherein L is the sequence length of the intrinsic mode function IMF i (n), i is the sequence number of the intrinsic mode function IMF i (n), and E(i) is the energy value of the intrinsic mode function IMF i (n) with the sequence number i.

[0053] Optionally, the formula for determining the noise component N(n) of the reconstructed baseband signal y(n) is:

[0054]

[0055] The formula for determining the signal component s(n) of the reconstructed baseband signal y(n) is:

[0056]

[0057] wherein h is the intrinsic mode function IMF iwherein n is the sequence number, M is the number of intrinsic mode functions, and r(n) is the residual signal.

[0058] In a second aspect, the present application provides an electronic device for signal denoising, comprising a memory, a transceiver, and a processor.

[0059] The memory is configured to store a computer program; the transceiver is configured to transceive data under the control of the processor; and the processor is configured to read the computer program in the memory and implement the steps of the method for signal denoising according to the first aspect.

[0060] In a third aspect, the present application provides an apparatus for signal denoising, comprising:

[0061] A decomposition module is configured to perform multi-layer empirical mode decomposition on a baseband signal y(n) obtained by down-converting an LFM-modulated pulse signal S(n), to obtain a plurality of intrinsic mode functions;

[0062] A reconstruction module is configured to reconstruct a signal component s(n) and a noise component N(n) of the baseband signal y(n) based on the intrinsic mode functions and energy values of the intrinsic mode functions;

[0063] A determination module is configured to determine a corresponding denoised signal z(n) based on amplitudes of discrete Fourier spectra of the reconstructed signal component s(n) and the reconstructed noise component N(n).

[0064] In a fourth aspect, the present application provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method for signal denoising according to the first aspect.

[0065] In a fifth aspect, the present application provides a computer program product comprising a computer program, wherein the computer program, when executed by a processor, implements the steps of the method for signal denoising according to the first aspect.

[0066] The method and apparatus for signal denoising provided by the present application can effectively realize adaptive threshold denoising of an LFM pulse signal superimposed with additive stationary noise in a low SNR condition, by using an empirical mode decomposition algorithm to decompose a baseband LFM signal to obtain a series of intrinsic mode functions, reconstructing a signal component and a noise component based on the intrinsic mode functions, and calculating Fourier spectra of the signal component and the noise component. BRIEF DESCRIPTION OF DRAWINGS

[0067] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0068] Figure 1 This is a flowchart illustrating the signal denoising method provided by the present invention;

[0069] Figure 2 This is a schematic diagram of the overall process of the signal denoising method provided by the present invention;

[0070] Figure 3 This is the energy distribution diagram of the intrinsic mode function provided by the present invention;

[0071] Figure 4 These are waveforms of the reconstructed low-frequency signal and the reconstructed noise signal provided by this invention;

[0072] Figure 5 These are the spectrum diagrams of the reconstructed low-frequency signal and the reconstructed noise signal provided by this invention;

[0073] Figure 6 This is a comparison chart of the decomposition and denoising effects of three different algorithms provided by this invention;

[0074] Figure 7 This is a schematic diagram of the structure of the electronic device provided by the present invention;

[0075] Figure 8 This is a schematic diagram of the signal denoising device provided by the present invention. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0077] The following is combined Figures 1-8 The present invention describes a method and apparatus for signal denoising.

[0078] Linear frequency modulation signal is a kind of large time width band width signal.The phase spectrum of linear frequency modulation signal has square law characteristic, and a larger compression ratio can be obtained in pulse compression process, and the biggest advantage is that the matching filter used is not sensitive to the Doppler frequency shift of echo signal, that is, one matching filter can be used to process echo signals with different Doppler frequency shifts, which will greatly simplify the radar signal processing system, and linear frequency modulation signal has good range resolution and radial velocity resolution.Therefore, linear frequency modulation signal is one of the signal waveforms often used in modern high-performance radar systems, and compared with other pulse compression signals, it is easy to produce by digital technology and mature in technology, so it can be widely used in engineering.Common radar signals use linear frequency modulation signal (LFM), which belongs to wideband signal and the frequency is variable, and it is not a linear stationary signal, and cannot be denoised by traditional Fourier transform.

[0079] And empirical mode decomposition algorithm is a data-driven adaptive decomposition algorithm.It has the following characteristics:

[0080] First, empirical mode decomposition is an approximate complete decomposition, and the difference between the reconstructed signal and the original signal is very small and almost negligible;

[0081] Second, empirical mode decomposition is an adaptive decomposition, which is completely driven by data without selecting basis functions;

[0082] Third, empirical mode decomposition is a multi-resolution decomposition, and the decomposition result is composed of different intrinsic mode functions with small to large time scale.

[0083] The above three characteristics make empirical mode decomposition very suitable for processing non-stationary signals such as LFM signals.

[0084] After receiving the low signal-to-noise ratio signal, the baseband LFM signal is demodulated, the baseband LFM signal is decomposed by using the empirical mode decomposition algorithm to obtain a series of intrinsic mode functions, the demarcation point of the signal component and the noise component in the intrinsic mode function is estimated, the signal component and the noise component are reconstructed according to the demarcation point of the intrinsic mode function, the discrete Fourier spectrum of the signal component and the noise component is calculated, the spectrum of the signal component is subtracted from the spectrum of the noise component, and finally the signal obtained by subtracting the spectrum is subjected to inverse Fourier transform to obtain the denoised signal.

[0085] Figure 1 It is the flowchart of the signal denoising method provided by the application; as Figure 1 The signal denoising method comprises the following steps:

[0086] Step 101, performing multi-layer empirical mode decomposition on a baseband signal y(n) obtained by down-converting an LFM modulated pulse signal S(n) to obtain a plurality of intrinsic mode functions;

[0087] Specifically, a common radar signal adopts a linear frequency modulation signal (LFM), which has the advantage of being insensitive to the Doppler shift of a return signal, i.e., a matched filter can be used to process return signals with different Doppler shifts, greatly simplifying the radar signal processing system. However, in actual applications, because the electromagnetic environment is becoming increasingly complex, higher requirements are placed on the recognition of radar signals. In order to more effectively improve the accuracy of radar signal recognition, it is necessary to perform denoising processing on the radar signal.

[0088] Generally, a transmitter transmits a continuous radio frequency signal, which is an LFM modulated pulse signal after up-conversion. A receiver receives the pulse signal at a certain sampling rate to obtain a corresponding LFM modulated discrete pulse signal. By down-converting the discrete pulse signal, a corresponding baseband signal y(n) is obtained, which is an intermediate frequency signal. The baseband signal is subjected to multi-layer empirical mode decomposition to obtain a plurality of intrinsic mode functions {IMF1(n), IMF2(n), …, IMF j (n)}, where j is the serial number of the intrinsic mode function. When j takes the maximum value, it represents the number of intrinsic mode functions.

[0089] Step 102, reconstructing a signal component s(n) and a noise component N(n) of the baseband signal y(n) based on the intrinsic mode functions and energy values of the intrinsic mode functions;

[0090] Specifically, the plurality of intrinsic mode functions {IMF1(n), IMF2(n), …, IMF jAfter (n), the energy value corresponding to each intrinsic mode function is determined, and then the energy value distribution of all intrinsic mode functions can be determined. If the energy value corresponding to a certain or certain special points in the energy value distribution has changed, such as the energy value of intrinsic mode function IMF1(n) is 50, the energy value of intrinsic mode function IMF2(n) is 60, and the energy value of intrinsic mode function IMF3(n) is 100 or 200, and the multi-layer empirical mode decomposition process is usually to decompose the signal from high to low frequency, so in the decomposition process, the noise component of high frequency is generally filtered out first, and then the signal component of low frequency. Considering that the energy of the signal is generally greater than or much greater than the energy of the noise, the intrinsic mode function with energy mutation can be determined according to the intrinsic mode function with energy mutation, and the signal component s(n) and the noise component N(n) of the baseband signal y(n) are reconstructed. It can be simply understood that the intrinsic mode function before the energy mutation represents the noise part of the baseband signal y(n), and the intrinsic mode function after the energy mutation represents the useful signal part including the baseband signal y(n). After the above method is processed, the noise is stripped in each sub-band, and the useful signal in other frequency bands is not affected, and the signal component s(n) of the reconstructed baseband signal y(n) contains less noise.

[0091] Step 103, based on the amplitude of the discrete Fourier spectrum of the reconstructed signal component s(n) and the amplitude of the discrete Fourier spectrum of the reconstructed noise component N(n), the corresponding denoised signal z(n) is determined.

[0092] Specifically, after the signal component s(n) and the noise component N(n) of the baseband signal y(n) are reconstructed, the noise component N(n) is more pure and clean, and does not contain the characteristics of the signal component. The discrete Fourier transform is used to determine the discrete Fourier spectrum of the signal component s(n) and the discrete Fourier spectrum of the noise component N(n). According to the spectral characteristics of the discrete Fourier spectrum, the amplitude of the discrete Fourier spectrum of the signal component s(n) and the amplitude of the discrete Fourier spectrum of the noise component N(n) are determined.

[0093] It can be understood that the denoised signal is usually obtained by subtracting the pure noise spectrum from the signal spectrum with noise. However, directly subtracting the two spectra may cause the useful signal of high frequency or low frequency to be removed. Therefore, in the present application, the amplitude of the discrete Fourier spectrum of the reconstructed signal component s(n) and the amplitude of the discrete Fourier spectrum of the reconstructed noise component N(n) are used to determine the amplitude of the denoised signal, and then the denoised signal is determined. The above situation that the useful signal is removed can be avoided.

[0094] The baseband signal y(n), the signal component s(n), the noise component N(n) and the denoised signal z(n) all represent discrete sequences, which are discrete sequences obtained at the same sampling frequency, n represents the sequence number of the discrete sequences, and the value range is [1, N] or [0, N-1]. N represents the length of all the sequences, and the sequence lengths of the baseband signal y(n), the signal component s(n), the noise component N(n) and the denoised signal z(n) are the same. It can be understood that n also represents different time points corresponding to the discrete signals obtained by sampling the continuous signals at a certain sampling frequency.

[0095] The signal denoising method provided by the application can realize adaptive threshold denoising of the LFM pulse signal superimposed with additive stationary noise by using the empirical mode decomposition algorithm to decompose the baseband LFM signal to obtain a series of intrinsic mode functions, reconstructing the signal component and the noise component by using the intrinsic mode functions, calculating the Fourier spectrum of the signal component and the noise component, and taking the spectrum amplitude of the noise intrinsic mode function in the empirical mode decomposition as the threshold for Fourier denoising of the signal component.

[0096] Optionally, the baseband signal y(n) obtained by down-converting the LFM modulated pulse signal S(n) is subjected to multi-layer empirical mode decomposition to obtain a plurality of intrinsic mode functions, including:

[0097] Based on the spline difference function, the upper envelope e max (n) corresponding to all the maximum values y max (n) of the baseband signal y(n) is determined, and the lower envelope e min (n) corresponding to all the minimum values y min (n) of the baseband signal y(n) is determined.

[0098] Based on the difference between the baseband signal y(n) and the average value m(n) of the upper and lower envelopes, a high-frequency detail signal d(n) is determined.

[0099] If it is determined that the high-frequency detail signal d(n) satisfies the intrinsic mode function condition, the high-frequency detail signal d(n) is determined as the intrinsic mode function IMF i (n) obtained by the multi-layer empirical mode decomposition.

[0100] Based on the difference between the baseband signal y(n) and the intrinsic mode function IMF i (n), a corresponding residual signal r(n) is determined.

[0101] If it is determined that the residual signal r(n) satisfies the end condition of the multi-layer empirical mode decomposition, all the intrinsic mode functions IMF i (n) corresponding to the plurality of intrinsic mode functions are determined.

[0102] Specifically, the empirical model decomposition process includes:

[0103] (S11) Let the baseband signal y(n) above be y*(n), and determine all the maxima of the y*(n) sequence. max (n) and all local minima y* min (n);

[0104] (S12) For all the above maxima y* max (n) and all local minima y* min (n) Using the spline interpolation function, the corresponding upper envelope e is formed. max (n) and lower envelope e min (n);

[0105] (S13) Calculate the average value m(n) of the upper and lower envelopes, that is, the average value of the upper and lower envelopes;

[0106] Optionally, the average value m(n) of the upper and lower envelopes is determined by a predefined formula, which is:

[0107]

[0108] Among them, e max (n) represents all the maxima of the baseband signal y(n). max (n) corresponds to the upper envelope, e min (n) represents all the minimum values ​​y* of the baseband signal y(n). min (n) corresponds to the lower envelope.

[0109] Specifically, y* max y*(n) is a sequence of all the maxima of y*(n), y* min y*(n) is the sequence of all the minimum values ​​of y*(n). y*(n) is another representation of the baseband signal y(n), i.e., y* max y* is a sequence of all the maxima of y(n). min y(n) is the sequence of all the minimum values ​​of y(n). max (n) The sequence is determined using cubic spline interpolation, y* max (n) The upper envelope e corresponding to the sequence max (n), for y* min (n) The sequence is determined using cubic spline interpolation, y* min (n) The lower envelope e corresponding to the sequence min (n), where n represents the sequence number in a sequence, and also represents different time points when a continuous signal is sampled at a certain sampling frequency. The upper envelope e above...max (n), lower envelope e min (n) and the average value m(n) sequence of upper and lower envelopes have the same length.

[0110] (S14) subtracting the average value m(n) of the upper and lower envelopes from the baseband signal y(n) to obtain a high-frequency detail signal d(n);

[0111] (S15) determining whether the high-frequency detail signal d(n) satisfies the intrinsic mode function condition, and if so, recording the high-frequency detail signal d(n) as the i th intrinsic mode function IMF i (n); wherein i is the serial number of the intrinsic mode function, and increases with the increase of the high-frequency detail signal d(n) satisfying the intrinsic mode function condition.

[0112] Optionally, in the embodiment of the present application, if it is determined that the high-frequency detail signal d(n) does not satisfy the intrinsic mode function condition, the high-frequency detail signal d(n) is used to update the baseband signal y(n);

[0113] that is, the high-frequency detail signal d(n) is replaced by y*(n), and steps S11 to S14 are repeated, wherein i is an integer greater than 0.

[0114] (S16) subtracting the intrinsic mode function obtained in step S15 from the baseband signal y(n) to obtain a residual signal r(n);

[0115] (S17) determining whether the residual signal r(n) satisfies the end condition of the empirical mode decomposition algorithm, and if so, the algorithm stops decomposing;

[0116] Optionally, in the embodiment of the present application, if it is determined that the residual signal r(n) does not satisfy the end condition of the multi-layer empirical mode decomposition, the residual signal r(n) is used to update the baseband signal y(n); and based on the updated residual signal r(n), a new residual signal r(n) is determined.

[0117] that is, when the residual signal r(n) does not satisfy the end condition of the multi-layer empirical mode decomposition, the above residual signal r(n) is replaced by y*(n), and steps S11 to S16 are repeated until the residual signal r(n) satisfies the end condition of the multi-layer empirical mode decomposition, and finally a plurality of intrinsic mode functions IMF1(n), IMF2(n)…IMF j (n) are obtained, wherein j is the number of intrinsic mode functions;

[0118] Optionally, the signal component s(n) and the noise component N(n) of the baseband signal y(n) are reconstructed based on the intrinsic mode function and the energy value of the intrinsic mode function, comprising:

[0119] determining an energy value corresponding to each of the eigenmode functions, and constructing an energy spectrum corresponding to all the eigenmode functions;

[0120] determining the serial number of the eigenmode function corresponding to the point of energy mutation in the energy spectrum, and taking the serial number as a boundary point;

[0121] determining a noise component N(n) of the reconstructed baseband signal y(n) based on the sum of all the eigenmode functions with serial numbers less than the boundary point;

[0122] determining a signal component s(n) of the reconstructed baseband signal y(n) based on the sum of all the eigenmode functions with serial numbers greater than or equal to the boundary point and the residual signal.

[0123] Specifically, after the LFM modulated pulse signal S(n) corresponding to a plurality of eigenmode functions is determined, the energy value of each of the eigenmode functions is determined respectively;

[0124] Optionally, in the embodiment of the present application, the determination of the energy value corresponding to each of the eigenmode functions and the construction of the energy spectrum corresponding to all the eigenmode functions comprise:

[0125] According to an energy formula, the energy value of each eigenmode function is determined to form a corresponding energy spectrum; the energy formula is:

[0126]

[0127] wherein L is the sequence length of the eigenmode function IMF i (n), i is the serial number of the eigenmode function IMF i (n), E(i) is the energy value of the eigenmode function IMF i (n) with the serial number i, and there are as many energy values as there are eigenmode functions. The sequence length L of the eigenmode function IMF i (n) is the same as the sequence length N of z(n).

[0128] According to the energy distribution of the eigenmode functions, i.e. the energy spectrum corresponding to the eigenmode functions, the point of energy mutation in the energy spectrum is determined, i.e. the energy value of the eigenmode function with which serial number and the energy values of the eigenmode functions before and after the serial number have a significant change, such as the energy value of the eigenmode function corresponding to the serial number before the serial number increases by about 5%-10%, while the energy value of the eigenmode function with the serial number increases by 30% or more. The above is only illustrative and does not limit the specific change range of the point of energy mutation.

[0129] The sequence number of the intrinsic mode function is determined as the corresponding demarcation point, the intrinsic mode function screened out before the demarcation point is regarded as a noise intrinsic mode function, the intrinsic mode function screened out after the demarcation point is regarded as a signal intrinsic mode function, the noise intrinsic mode functions are added to obtain a reconstructed noise component N(n), the signal intrinsic mode functions are added and the residual signal r(n) is added to obtain a reconstructed signal component s(n). Assuming that the demarcation point determined above is h, that is, the sequence number of the intrinsic mode function is h, the reconstructed noise component N(n) and the reconstructed signal component s(n) can be expressed by the following formula:

[0130]

[0131] wherein h is the sequence number of the intrinsic mode function IMF i (n) corresponding to the point of energy mutation in the energy spectrum of the intrinsic mode function, r(n) is a residual signal, and M is the number of intrinsic mode functions IMF i (n), that is, the value of M is the number of the intrinsic mode functions IMF i (n) obtained by the multi-layer empirical mode decomposition. For example, the intrinsic mode functions include {IMF1(n), IMF2(n), …, IMF9(n)}, and the number of the intrinsic mode functions is 9, so the value of M is 9.

[0132] For example, the point of energy mutation in the energy spectrum of the intrinsic mode function is i=4, so the reconstructed noise component N(n)=IMF1(n)+IMF2(n)+IMF3(n), the reconstructed signal component s(n)=IMF4(n)+IMF5(n)+IMF6(n)+IMF7(n)+IMF8(n)+IMF9(n)+r(n), and n is the sequence number of the reconstructed noise component N(n) and the reconstructed signal component s(n), which also represents the time point corresponding to the sequence.

[0133] Optionally, the amplitude of the discrete Fourier spectrum of the reconstructed signal component s(n) and the amplitude of the discrete Fourier spectrum of the reconstructed noise component N(n) are used to determine a corresponding denoised signal z(n), including:

[0134] The discrete Fourier spectrum of the reconstructed signal component s(n) and the discrete Fourier spectrum of the reconstructed noise component N(n) are determined based on the discrete Fourier transform;

[0135] The amplitude of the denoised signal z(n) is determined based on the amplitude of the discrete Fourier spectrum of the signal component s(n) and the amplitude of the discrete Fourier spectrum of the noise component N(n);

[0136] The denoised signal z(n) is determined by performing inverse discrete Fourier transform on the amplitude of the denoised signal z(n).

[0137] Specifically, the reconstructed noise component N(n) corresponding to the baseband signal y(n) is determined, and the reconstructed signal component s(n) is determined. According to the discrete Fourier transform, the spectral representation of the reconstructed noise component N(n) and the reconstructed signal component s(n) is respectively determined as:

[0138]

[0139] Wherein, N is the length of the processed signal sequence, the length of the corresponding reconstructed noise component N(n) sequence when processing the noise component N(n); the length of the corresponding reconstructed signal component s(n) sequence when processing the signal component s(n), n is the sequence number of the s(n) sequence or the N(n) sequence, k is the signal frequency domain component, and F[] is the Fourier transform. And the length of the noise component N(n) sequence, the length of the noise component N(n) sequence and the length of the baseband signal y(n) sequence are the same.

[0140] Then, the amplitude of the discrete Fourier spectrum of the signal component s(n) can be represented as |F[s(n)]|, and the amplitude of the discrete Fourier spectrum of the noise component N(n) can be represented as |F[N(n)]|; wherein, |·| represents the modulo operation. Then, according to the size of |F[s(n)]| and |F[N(n)]|, the amplitude Z(n) of the denoised signal z(n) is determined; and based on the amplitude Z(n), the denoised signal z(n) is determined by inverse discrete Fourier transform.

[0141] Optionally, the amplitude of the denoised signal z(n) is determined based on the size of the amplitude of the discrete Fourier spectrum of the signal component s(n) and the amplitude of the discrete Fourier spectrum of the noise component N(n), comprising:

[0142] If the amplitude of the discrete Fourier spectrum of the signal component s(n) is greater than the amplitude of the discrete Fourier spectrum of the noise component N(n), then the difference between the two amplitudes is determined as the amplitude of the denoised signal z(n);

[0143] If the amplitude of the discrete Fourier spectrum of the signal component s(n) is less than or equal to the amplitude of the discrete Fourier spectrum of the noise component N(n), then the amplitude of the denoised signal z(n) is determined as zero.

[0144] Specifically, the amplitude Z(n) of the denoised signal z(n) can be represented by the formula:

[0145]

[0146] Wherein, n is the sequence number of s(n) sequence or N(n) sequence, F[] is Fourier transform. The n corresponding to signal component s(n) and noise component N(n) is the same, which is determined according to original sampling signal, that is, the length of baseband signal y(n) sequence determines the value range of n subscript.

[0147] Optionally, the amplitude of the de-noised signal z(n) is inversely discrete Fourier transformed to determine the de-noised signal z(n), and the specific formula is as follows:

[0148]

[0149] Wherein, Z(n) is the amplitude of the de-noised signal z(n), N is the sequence length of z(n), n is the sequence number of z(n) sequence, k is signal frequency domain component, F -1 [] is inverse discrete Fourier transform. And the length of baseband signal y(n) sequence and the length of de-noised signal z(n) sequence are the same.

[0150] Optionally, the intrinsic mode function satisfies the following conditions:

[0151] In the entire time range corresponding to the LFM modulated pulse signal S(n), the number of all maximum values y max (n) and the number of all minimum values y min (n) are equal to or differ by one from the number of zero-crossing points of baseband signal y(n);

[0152] And in any time period, the average value m(n) of the upper and lower envelopes is zero.

[0153] Optionally, the end condition of the multi-layer empirical mode decomposition is that the residual signal is a monotonic function or the maximum value of the residual signal r(n) is less than a specified threshold SD, and the specified threshold SD and the intrinsic mode function IMF i (n) are one-to-one corresponding.

[0154] Specifically, each intrinsic mode function IMF i (n) corresponds to a specified threshold SD, and the calculation formula of the specified threshold SD is as follows:

[0155]

[0156] Wherein, h(.) is Hilbert transform, the range 0~T is the length of entire pulse signal, that is, the length of baseband signal y(n) sequence or the length of intrinsic mode function IMF i (n). And h i (t) is the Hilbert transform of intrinsic mode function IMF i (n). The length of baseband signal y(n) sequence and the length of intrinsic mode function IMFi (n) is the same as the length of (n).

[0157] Optionally, the LFM modulated pulse signal S(n) is received by the receiver at a sampling rate f s The discrete signal obtained by receiving the radio frequency signal S(t), wherein the sampling rate f s is greater than the Nyquist sampling rate.

[0158] Optionally, the spline difference function is a cubic spline difference.

[0159] Cubic Spline Interpolation (Cubic Spline Interpolation) is a smooth curve through a series of shape value points, and the process of obtaining a curve function group by solving a three-bending moment equation group. The present application uses cubic spline difference to increase the length of the sampling signal sequence to the length of the original signal sequence, so that the corresponding data curve is smoother and the error is smaller.

[0160] The signal denoising method provided by the present application uses empirical mode decomposition algorithm to decompose a series of intrinsic mode functions from the baseband LFM signal, reconstructs the signal component and the noise component by using the above intrinsic mode function, calculates the Fourier spectrum of the signal component and the noise component, and uses the spectrum amplitude of the noise intrinsic mode function in the empirical mode decomposition as the threshold value of the signal component Fourier denoising, so that the adaptive threshold denoising is realized, and the LFM pulse signal superimposed with additive stationary noise can be effectively denoised in the case of low signal-to-noise ratio.

[0161] Figure 2 is the overall flowchart of the signal denoising method provided by the present application, as Figure 2 shown, the specific steps of the method are as follows:

[0162] Step one: the transmitter transmits a radio frequency signal, which is an LFM modulated pulse signal after up-conversion, and the radio frequency signal is denoted as S(t).

[0163] Step two: the receiver receives the radio frequency signal S(t) at a sampling rate f s The discrete signal S(n) is obtained by receiving the radio frequency signal S(t), and the intermediate frequency signal y(n) is obtained by down-conversion, and then the empirical mode decomposition is applied to the intermediate frequency signal y(n) to obtain a series of intrinsic mode functions.

[0164] Step three: estimate the demarcation point between the signal dominant component and the noise dominant component of the intrinsic mode function obtained in step two, then reconstruct the high frequency noise component and the low frequency signal component, obtain the reconstructed noise component N(n) and the reconstructed signal component s(n) and calculate the frequency spectrum F[N(n)], F[s(n)] of both. Then do spectral subtraction to F[N(n)], F[s(n)], and apply inverse Fourier transform to the signal obtained after spectral subtraction to obtain the de-noised signal.

[0165] In step two, the sampling rate of the receiver is greater than the Nyquist sampling rate. The empirical mode decomposition specifically includes the following sub-steps:

[0166] Sub-step 1: Let the signal y(n) be y*(n), find all the maximum values y max (n) and minimum values y min (n) of y*(n).

[0167] Sub-step 2: Use a spline interpolation function to form the lower envelope e min (n) and the upper envelope e max (n) for the minimum values y min (n) and the maximum values y max (n).

[0168] Sub-step 3: Calculate the average value m(n) of the upper envelope and the lower envelope, specifically represented as:

[0169]

[0170] Sub-step 4: Let y(n) minus m(n) to calculate the high frequency detail signal d(n), specifically represented as:

[0171] d(n) = y(n) - m(n);

[0172] Sub-step 5: Determine whether d(n) satisfies the condition for the intrinsic mode function to be valid. If it does, record d(n) as the i-th intrinsic mode function IMF i (n), otherwise, substitute d(n) into y*(n) and repeat steps S11 to S14, where i takes an integer greater than 0.

[0173] Sub-step 6: Let y(n) minus the intrinsic mode function obtained in (S15) to obtain the residual signal r(n), represented as: r(n) = y(n) - IMF i (n);

[0174] Sub-step 7: judging whether r(n) satisfies the end condition of the empirical mode decomposition, if yes, the algorithm stops decomposition, otherwise, y(n) is equal to r(n) and steps S11 to S16 are repeated until the residual signal r(n) satisfies the end condition of the empirical mode decomposition, and finally a series of intrinsic mode functions IMF1(n), IMF2(n), …, IMFj(n) are obtained, where j is the number of intrinsic mode functions. The end threshold of the empirical mode decomposition is expressed as: j i i i i Step three, the denoising processing of the intrinsic mode functions obtained by the empirical mode decomposition specifically includes the following sub-steps: i i Sub-step 1: calculating the energy of different intrinsic mode functions max max The energy of different intrinsic mode functions can be obtained by square summing the series of intrinsic mode functions obtained by the empirical mode decomposition, which is specifically expressed as: min min i i i where L is the sequence length of the intrinsic mode function IMF -1 (n), i is the serial number of the intrinsic mode function IMF max (n), and E(i) is the energy value of the intrinsic mode function IMF min (n) with the serial number i. The sequence length L of the intrinsic mode function IMF i (n) is the same as the sequence length N of z(n). i i Sub-step 2: estimating the critical point of the signal dominant component and the noise dominant component i The energy of different intrinsic mode functions IMF i (n) obtained by the multi-layer empirical mode decomposition is expressed as: i i It can be seen that the energy of the intrinsic mode function produces a strong mutation at IMF4. Because the process of the empirical mode decomposition in step one is to decompose the signal from high to low frequency, the noise components with high frequency are generally filtered out first, and then the signal components with low frequency are filtered out. Considering that the energy of the signal is generally greater than that of the noise, we can regard the components after IMF4 as useful signal components, and IMF1, IMF2 and IMF3 before IMF4 as noise components. i s Sub-step 3: reconstructing the noise signal and the low-frequency signal, and the corresponding formula is expressed as: s max ​

[0184] Wherein, h is the intrinsic mode function IMF corresponding to the point of energy sudden change in the intrinsic mode function energy spectrum i (n) is the sequence number, M is the number of intrinsic mode functions, and r(n) is the residual signal.

[0185] As shown in Figure 4 , the waveform diagram of the reconstructed noise signal (noise component) N(n) is shown in Figure 4-1 , the waveform diagram of the reconstructed low-frequency signal (signal component) s(n) is shown in Figure 4-2 , and the zoomed-in display of the waveform diagram in the oval frame is shown in Figure 4-3 , and the zoomed-in display of the waveform diagram in the oval frame is shown in Figure 4-1 . Figure 4-4 , the zoomed-in display of the waveform diagram in the oval frame is shown in Figure 4-2 . As can be seen from Figure 4-3 , the waveform of the reconstructed low-frequency signal can effectively display the characteristics of the signal waveform, but there are still some burrs in the local area, which indicates that there is still some residual low-frequency noise, which can be further denoised through the subsequent steps.

[0186] Sub-step 4: Calculate the frequency spectrum of the reconstructed noise signal (noise component) N(n) and the frequency spectrum of the reconstructed low-frequency signal (signal component) s(n), which can be specifically represented as:

[0187]

[0188]

[0189] Wherein, N is the sequence length of the baseband signal y(n), n is the sequence number of the N(n) sequence or the s(n) sequence, k is the signal frequency domain component, and F[] is the Fourier transform. The sequence numbers n of the N(n) sequence or the s(n) sequence are the same, and the range is [0, N-1].

[0190] As shown in Figure 5 , the frequency spectrum of the reconstructed low-frequency signal and the reconstructed noise signal provided by the application is shown in Figure 5-1 , the frequency spectrum of the reconstructed low-frequency signal and the reconstructed noise signal provided by the application is shown in Figure 5-2 , and the zoomed-in display of the oval frame is shown in Figure 5-1 . As can be seen from Figure 5-1 , the frequency spectrum of the reconstructed noise signal (noise component) N(n) has a tail at low frequency. Since the power of white noise is uniformly distributed in the frequency domain, the tail value is generally smaller than the low-frequency noise spectrum value contained in the reconstructed noise signal. Details can be checked in Figure 5-2 . This makes the reconstructed low-frequency signal (signal component) s(n) and the reconstructed noise signal (noise component) N(n) after spectral subtraction, remove the low-frequency noise under the premise of reducing signal loss, thereby realizing further denoising.

[0191] Sub-step 5, performing spectral subtraction on the spectrum of the reconstructed noise signal (noise component) N(n) and the reconstructed low-frequency signal (signal component) s(n);

[0192] The amplitude Z(n) of the de-noised signal z(n) obtained by subtracting the spectral amplitudes is represented as:

[0193]

[0194] Wherein, n is the sequence number of the N(n) sequence or the s(n) sequence, and the sequence numbers n of the N(n) sequence or the s(n) sequence are the same.

[0195] Sub-step 6, inverse Fourier transform to obtain the de-noised signal z(n) represented as:

[0196]

[0197] Figure 6 is the comparison chart of the de-noising effects of the three different algorithms provided by the present application, as shown in Figure 6 The same radar LFM signal is simulated by simulation software, and the de-noising results obtained according to the three different algorithms are compared, as shown in Figure 6 The de-noising effects of the empirical mode decomposition, the empirical mode decomposition combined with wavelet decomposition, and the empirical mode decomposition adaptive threshold de-noising algorithm proposed by the present application under different signal-to-noise ratios are shown in the comparison chart, and it can be seen that the method proposed by the present application has a smaller mean square error, which indicates that the signal de-noising method provided by the present application has better de-noising effect.

[0198] Figure 7 An example of an entity structure diagram of an electronic device is shown in Figure 7 The electronic device can include a processor 710, a communication interface 720, a memory 730, and a communication bus 740, wherein the processor 710, the communication interface 720, and the memory 730 can communicate with each other through the communication bus 740. The processor 710 can call the computer program in the memory 730 to execute the steps of the signal de-noising method, for example, including:

[0199] The baseband signal y(n) obtained by down-converting the LFM modulated pulse signal S(n) is subjected to multi-layer empirical mode decomposition to obtain a plurality of intrinsic mode functions;

[0200] Based on the intrinsic mode functions and the energy values of the intrinsic mode functions, the signal component s(n) and the noise component N(n) of the baseband signal y(n) are reconstructed;

[0201] Based on the amplitude of the discrete Fourier spectrum of the reconstructed signal component s(n) and the amplitude of the discrete Fourier spectrum of the reconstructed noise component N(n), a corresponding denoised signal z(n) is determined.

[0202] Optionally, the baseband signal y(n) obtained by down-converting the LFM modulated pulse signal S(n) is subjected to multi-layer empirical mode decomposition to obtain a plurality of intrinsic mode functions, including:

[0203] Based on the spline difference function, all maximum values y max (n) of the baseband signal y(n) are determined, and the corresponding upper envelope e max (n) is determined, and all minimum values y min (n) of the baseband signal y(n) are determined, and the corresponding lower envelope e min (n) is determined.

[0204] Based on the difference between the baseband signal y(n) and the average value m(n) of the upper and lower envelopes, a high-frequency detail signal d(n) is determined.

[0205] If it is determined that the high-frequency detail signal d(n) satisfies the intrinsic mode function condition, the high-frequency detail signal d(n) is determined as the intrinsic mode function IMF i (n) obtained by the multi-layer empirical mode decomposition.

[0206] Based on the difference between the baseband signal y(n) and the intrinsic mode function IMF i (n), a corresponding residual signal r(n) is determined.

[0207] If it is determined that the residual signal r(n) satisfies the end condition of the multi-layer empirical mode decomposition, all intrinsic mode functions IMF i (n) are determined to constitute the plurality of intrinsic mode functions.

[0208] Optionally, the steps further include:

[0209] If it is determined that the high-frequency detail signal d(n) does not satisfy the intrinsic mode function condition, the high-frequency detail signal d(n) is used to update the baseband signal y(n).

[0210] Based on the updated baseband signal y(n), a new high-frequency detail signal d(n) is determined.

[0211] Optionally, the steps further include:

[0212] If it is determined that the residual signal r(n) does not satisfy the end condition of the multi-layer empirical mode decomposition, the residual signal r(n) is used to update the baseband signal y(n).

[0213] Based on the updated residual signal r(n), a new residual signal r(n) is determined.

[0214] Optionally, the reconstructing the signal component s(n) and the noise component N(n) of the baseband signal y(n) based on the eigenmode functions and the energy values of the eigenmode functions comprises:

[0215] Determining the energy value corresponding to each of the eigenmode functions, and constructing an energy spectrum corresponding to all the eigenmode functions;

[0216] Determining the serial number of the eigenmode function corresponding to the point of energy mutation in the energy spectrum, and taking the serial number as a boundary point;

[0217] Based on the sum of all the eigenmode functions with serial numbers less than the boundary point, the noise component N(n) of the reconstructed baseband signal y(n) is determined;

[0218] Based on the sum of all the eigenmode functions with serial numbers greater than or equal to the boundary point, and the residual signal, the signal component s(n) of the reconstructed baseband signal y(n) is determined.

[0219] Optionally, the determining the corresponding denoised signal z(n) based on the amplitude of the discrete Fourier spectrum of the reconstructed signal component s(n) and the amplitude of the discrete Fourier spectrum of the reconstructed noise component N(n) comprises:

[0220] Based on the discrete Fourier transform, the discrete Fourier spectrum of the reconstructed signal component s(n) and the discrete Fourier spectrum of the reconstructed noise component N(n) are respectively determined;

[0221] Based on the size of the amplitude of the discrete Fourier spectrum of the signal component s(n) and the amplitude of the discrete Fourier spectrum of the noise component N(n), the amplitude of the denoised signal z(n) is determined;

[0222] The amplitude of the denoised signal z(n) is subjected to inverse discrete Fourier transform to determine the denoised signal z(n).

[0223] Optionally, the determining the amplitude of the denoised signal z(n) based on the size of the amplitude of the discrete Fourier spectrum of the signal component s(n) and the amplitude of the discrete Fourier spectrum of the noise component N(n) comprises:

[0224] If the amplitude of the discrete Fourier spectrum of the signal component s(n) is greater than the amplitude of the discrete Fourier spectrum of the noise component N(n), then the difference between the two amplitudes is determined as the amplitude of the denoised signal z(n);

[0225] If the amplitude of the discrete Fourier spectrum of the signal component s(n) is less than or equal to the amplitude of the discrete Fourier spectrum of the noise component N(n), then the amplitude of the de-noised signal z(n) is determined to be zero.

[0226] Optionally, the amplitude of the de-noised signal z(n) is subjected to inverse discrete Fourier transform to determine the de-noised signal z(n), and the specific formula is:

[0227]

[0228] wherein Z(n) is the amplitude of the de-noised signal z(n), N is the sequence length of z(n), n is the sequence number of the sequence z(n), k is the signal frequency domain component, F -1 [] is the inverse discrete Fourier transform.

[0229] Optionally, the condition for the intrinsic mode function to be valid includes:

[0230] In the entire time range corresponding to the LFM modulated pulse signal S(n), the number of all maximum values y max (n) and the number of all minimum values y min (n) are equal to or differ by one from the number of zero-crossing points of the baseband signal y(n).

[0231] And in any time period, the average value m(n) of the upper and lower envelopes is zero.

[0232] Optionally, the end condition of the multi-layer empirical mode decomposition is that the residual signal is a monotonic function or the maximum value of the residual signal r(n) is less than a specified threshold SD, and the specified threshold SD and the intrinsic mode function IMF i (n) are in one-to-one correspondence.

[0233] Optionally, the specified threshold SD and the intrinsic mode function IMF i (n) are in one-to-one correspondence, and the specific correspondence is:

[0234]

[0235] wherein h i (t) is the Hilbert transform of the intrinsic mode function IMF i (n), and the range 0-T is the length of the entire intrinsic mode function IMF i (n) or the length of the intrinsic mode function IMF i (n), i is the sequence number of the intrinsic mode function IMF i (n). The length of the baseband signal y(n) sequence and the length of the intrinsic mode function IMF i (n) are the same.

[0236] Optionally, the LFM modulated pulse signal S(n) is received by the receiver at a sampling rate f s The discrete signal obtained by receiving the radio frequency signal S(t), wherein the sampling rate f s is greater than the Nyquist sampling rate.

[0237] Optionally, the spline difference function is a cubic spline difference.

[0238] Optionally, the average value m(n) of the upper and lower envelopes is determined by a predefined formula, and the predefined formula is:

[0239]

[0240] wherein e max (n) is the upper envelope corresponding to all the maximum values y max (n) of the baseband signal y(n), e min (n) is the lower envelope corresponding to all the minimum values y min (n) of the baseband signal y(n).

[0241] Optionally, the energy value corresponding to each intrinsic mode function is determined, and an energy spectrum corresponding to all the intrinsic mode functions is constructed, including:

[0242] According to an energy formula, the energy value of each intrinsic mode function is determined to form a corresponding energy spectrum; and the energy formula is:

[0243] L is the sequence length of the intrinsic mode function IMF i (n), i is the serial number of the intrinsic mode function IMF i (n), E(i) is the energy value of the intrinsic mode function IMF i (n) with the serial number i.

[0244] Optionally, the formula for determining the noise component N(n) of the reconstructed baseband signal y(n) is:

[0245] The formula for determining the signal component s(n) of the reconstructed baseband signal y(n) is:

[0246]

[0247] wherein h is the intrinsic mode function IMF i (n) corresponding to the point of energy mutation in the intrinsic mode function energy spectrum, i is the serial number of the intrinsic mode function IMF i (n), M is the number of intrinsic mode functions, and r(n) is the residual signal.

[0248] Moreover, the logic instructions in the memory 730 described above can be implemented in the form of software function units and sold or used as independent products, and can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the parts that make contributions to the prior art or parts of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage medium includes various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, etc.

[0249] It should be noted that the electronic device provided by the present application can realize all the method steps realized by the method embodiments described above, and can achieve the same technical effects. Here, the same parts and beneficial effects of the electronic device provided by the present application and the signal denoising method embodiments provided by the present application will not be described in detail.

[0250] The signal denoising device provided by the present application is described below. The signal denoising device described below can be referred to each other corresponding to the signal denoising method described above.

[0251] Figure 8 The signal denoising device provided by the present application is described below. The signal denoising device described below can be referred to each other corresponding to the signal denoising method described above. Figure 8 As shown in the figure, the device comprises:

[0252] The decomposition module 801 is configured to perform multi-layer empirical mode decomposition on the baseband signal y(n) obtained by down-converting the LFM modulated pulse signal S(n), to obtain a plurality of intrinsic mode functions;

[0253] The reconstruction module 802 is configured to reconstruct the signal component s(n) and the noise component N(n) of the baseband signal y(n) based on the intrinsic mode functions and the energy values of the intrinsic mode functions;

[0254] The determination module 803 is configured to determine the corresponding denoised signal z(n) based on the amplitudes of the discrete Fourier spectrum of the reconstructed signal component s(n) and the amplitudes of the discrete Fourier spectrum of the reconstructed noise component N(n).

[0255] Optionally, the decomposition module 801 is further configured to:

[0256] determine all the maximum values y*(n) of the baseband signal y(n) corresponding to the upper envelope e max (n) based on the spline difference function.max (n), and all minima y min (n) of the baseband signal y(n) correspond to the lower envelope e min (n);

[0257] determine a high frequency detail signal d(n) based on the difference between the baseband signal y(n) and the average value m(n) of the upper and lower envelopes;

[0258] if it is determined that the high frequency detail signal d(n) satisfies the condition for the existence of the intrinsic mode function, then determine that the high frequency detail signal d(n) is an intrinsic mode function IMF i (n) obtained by the multi-layer empirical mode decomposition;

[0259] determine a corresponding residual signal r(n) based on the difference between the baseband signal y(n) and the intrinsic mode function IMF i (n);

[0260] if it is determined that the residual signal r(n) satisfies the end condition of the multi-layer empirical mode decomposition, then determine that all intrinsic mode functions IMF i (n) correspond to the plurality of intrinsic mode functions.

[0261] Optionally, the decomposition module 801 is further configured to:

[0262] if it is determined that the high frequency detail signal d(n) does not satisfy the condition for the existence of the intrinsic mode function, then update the baseband signal y(n) with the high frequency detail signal d(n);

[0263] determine a new high frequency detail signal d(n) based on the updated baseband signal y(n).

[0264] Optionally, the decomposition module 801 is further configured to:

[0265] if it is determined that the residual signal r(n) does not satisfy the end condition of the multi-layer empirical mode decomposition, then update the baseband signal y(n) with the residual signal r(n);

[0266] determine a new residual signal r(n) based on the updated residual signal r(n).

[0267] Optionally, the reconstruction module 802 is further configured to:

[0268] determine the energy value corresponding to each intrinsic mode function, and construct an energy spectrum corresponding to all intrinsic mode functions;

[0269] determine the serial number of the intrinsic mode function corresponding to the point where the energy mutation occurs in the energy spectrum, and use the serial number as a demarcation point;

[0270] determine the noise component N(n) of the reconstructed baseband signal y(n) based on the sum of eigenmode functions whose serial numbers are less than the serial number of the boundary point;

[0271] determine the signal component s(n) of the reconstructed baseband signal y(n) based on the sum of eigenmode functions whose serial numbers are greater than or equal to the serial number of the boundary point, and the residual signal.

[0272] Optionally, the determining module 803 is further configured to:

[0273] determine the discrete Fourier spectrum of the reconstructed signal component s(n) and the discrete Fourier spectrum of the reconstructed noise component N(n) based on the discrete Fourier transform;

[0274] determine the amplitude of the de-noised signal z(n) based on the amplitude of the discrete Fourier spectrum of the signal component s(n) and the amplitude of the discrete Fourier spectrum of the noise component N(n).

[0275] perform inverse discrete Fourier transform on the amplitude of the de-noised signal z(n) to determine the de-noised signal z(n).

[0276] Optionally, the determining module 803 is further configured to:

[0277] if the amplitude of the discrete Fourier spectrum of the signal component s(n) is greater than the amplitude of the discrete Fourier spectrum of the noise component N(n), then determine the difference between the two amplitudes as the amplitude of the de-noised signal z(n);

[0278] if the amplitude of the discrete Fourier spectrum of the signal component s(n) is less than or equal to the amplitude of the discrete Fourier spectrum of the noise component N(n), then determine the amplitude of the de-noised signal z(n) as zero.

[0279] Optionally, the performing inverse discrete Fourier transform on the amplitude of the de-noised signal z(n) to determine the de-noised signal z(n) is specifically as follows:

[0280]

[0281] wherein Z(n) is the amplitude of the de-noised signal z(n), N is the sequence length of z(n), n is the serial number of the sequence of z(n), k is the signal frequency domain component, and F -1 [] is the inverse discrete Fourier transform.

[0282] Optionally, the eigenmode function condition comprises:

[0283] all the maximum values y* of the LFM modulated pulse signal S(n) in the entire time range corresponding to the LFM modulated pulse signal S(n) are greater than the sum of the maximum values of the noise component N(n) in the entire time range corresponding to the LFM modulated pulse signal S(n). maxThe sum of the number of (n) is equal to or differs by one from the number of zero-crossings of the baseband signal y(n). min The sum of the number of (n) is equal to or differs by one from the number of zero-crossings of the baseband signal y(n).

[0284] And the average value m(n) of the upper and lower envelopes is zero at any time period.

[0285] Optionally, the end condition of the multi-layer empirical mode decomposition is that the residual signal is a monotonic function or the maximum value of the residual signal r(n) is less than a specified threshold SD, and the specified threshold SD and the intrinsic mode function IMF i (n) are one-to-one corresponding.

[0286] Optionally, the specified threshold SD and the intrinsic mode function IMF i (n) are one-to-one corresponding, and the specific correspondence is:

[0287]

[0288] Wherein, h i (t) is the Hilbert transform of the intrinsic mode function IMF i (n), and the range 0~T is the length of the entire intrinsic mode function IMF i (n), i is the serial number of the intrinsic mode function IMF i (n).

[0289] Optionally, the LFM modulated pulse signal S(n) is a discrete signal obtained by receiving a radio frequency signal S(t) with a sampling rate f s , wherein the sampling rate f s is greater than the Nyquist sampling rate.

[0290] Optionally, the spline difference function is a cubic spline difference.

[0291] Optionally, the average value m(n) of the upper and lower envelopes is determined by a pre-defined formula, and the pre-defined formula is:

[0292]

[0293] Wherein, e max (n) is the maximum value y max (n) corresponding to the upper envelope, e min (n) is the minimum value y min (n) corresponding to the lower envelope.

[0294] Optionally, the determination of the energy value corresponding to each intrinsic mode function and the construction of the energy spectrum corresponding to all intrinsic mode functions include:

[0295] According to an energy formula, an energy value of each intrinsic mode function is determined to form a corresponding energy spectrum; the energy formula is:

[0296] L is an intrinsic mode function IMF i (n) is a sequence length, i is a serial number of the intrinsic mode function IMF i (n) is a serial number of the intrinsic mode function IMF i (n) is an energy value of the intrinsic mode function IMF

[0297] Optionally, a formula for determining the noise component N(n) of the reconstructed baseband signal y(n) is:

[0298]

[0299] A formula for determining the signal component s(n) of the reconstructed baseband signal y(n) is:

[0300]

[0301] Wherein, h is an intrinsic mode function IMF corresponding to a point of energy mutation in the intrinsic mode function energy spectrum i (n) is a serial number of the intrinsic mode function IMF

[0302] It should be noted that the division of units in the embodiments of the present application is illustrative, and is only a logical functional division. In actual implementation, another division manner can be used. In addition, each functional unit in each embodiment of the present application can be integrated in one processing unit, or each unit can exist physically, or two or more units can be integrated in one unit. The integrated unit can be realized in the form of hardware or in the form of a software functional unit.

[0303] The integrated unit, if implemented in the form of a software function unit and sold or used as an independent product, can be stored in a processor-readable storage medium. Based on such understanding, the technical solutions of the present application or all or part of the technical solutions that essentially contribute to the prior art can be embodied in the form of a software product. The computer software product is stored in a storage medium, and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to perform all or part of the steps of the methods described in various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0304] It should be noted that the signal denoising device provided by the present application can realize all the method steps realized by the method embodiments and achieve the same technical effects. Therefore, the same parts and beneficial effects of the signal denoising device provided by the present application as the method embodiments will not be described in detail.

[0305] On the other hand, the present application also provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium, and the computer program includes program instructions. When the program instructions are executed by a computer, the computer can execute the steps of the signal denoising method provided by the above-mentioned methods, for example, including:

[0306] The baseband signal y(n) obtained by down-converting the LFM modulated pulse signal S(n) is subjected to multi-layer empirical mode decomposition to obtain a plurality of intrinsic mode functions;

[0307] Based on the intrinsic mode functions and the energy values of the intrinsic mode functions, the signal component s(n) and the noise component N(n) of the baseband signal y(n) are reconstructed;

[0308] Based on the amplitude of the discrete Fourier spectrum of the reconstructed signal component s(n) and the amplitude of the discrete Fourier spectrum of the reconstructed noise component N(n), the corresponding denoised signal z(n) is determined.

[0309] On the other hand, the processor-readable storage medium provided by the embodiments of the present application stores a computer program, and the computer program is used to make the processor execute the signal denoising method provided by the above-mentioned embodiments, for example, including:

[0310] The baseband signal y(n) obtained by down-converting the LFM modulated pulse signal S(n) is subjected to multi-layer empirical mode decomposition to obtain a plurality of intrinsic mode functions;

[0311] Based on the intrinsic mode functions and energy values of the intrinsic mode functions, a signal component s(n) and a noise component N(n) of the baseband signal y(n) are reconstructed;

[0312] Based on the amplitude of the discrete Fourier spectrum of the reconstructed signal component s(n) and the amplitude of the discrete Fourier spectrum of the reconstructed noise component N(n), a corresponding denoised signal z(n) is determined.

[0313] The processor-readable storage medium can be any available medium or data storage device that the processor can access, including but not limited to a magnetic storage (such as a floppy disk, a hard disk, a magnetic tape, a magneto-optical disk (MO), etc.), an optical storage (such as a CD, a DVD, a BD, a HVD, etc.), and a semiconductor memory (such as a ROM, an EPROM, an EEPROM, a non-volatile memory (NAND FLASH), a solid state disk (SSD)), etc.

[0314] The device embodiments described above are merely illustrative, wherein the units described as separate components can or can not be physically separated, and the components displayed as units can or can not be physical units, i.e., they can be located in one place or distributed on multiple network units. Part or all of the modules can be selected to achieve the purposes of the embodiments according to actual needs. Those skilled in the art can understand and implement it without creative labor.

[0315] From the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be realized by means of software plus necessary universal hardware platforms, and of course, can also be realized by hardware. Based on such understanding, the above technical solutions, essentially or in other words, the part that contributes to the prior art, can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, etc., and includes a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute the methods described in the various embodiments or some parts of the embodiments.

[0316] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit the same; and although the present application has been described in detail with reference to the foregoing embodiments, it should be appreciated by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features thereof can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method of signal denoising, characterized by, The method comprises: performing multi-layer empirical mode decomposition on a baseband signal y(n) obtained by down-converting an LFM modulated pulse signal S(n) to obtain a plurality of intrinsic mode functions; reconstructing a signal component s(n) and a noise component N(n) of the baseband signal y(n) based on the intrinsic mode functions and energy values of the intrinsic mode functions; determining a corresponding denoised signal z(n) based on amplitudes of discrete Fourier spectra of the reconstructed signal component s(n) and the reconstructed noise component N(n), wherein the determination comprises: if the amplitude of the discrete Fourier spectrum of the signal component s(n) is greater than the amplitude of the discrete Fourier spectrum of the noise component N(n), then determining a difference between the two amplitudes as the amplitude of the denoised signal z(n); if the amplitude of the discrete Fourier spectrum of the signal component s(n) is less than or equal to the amplitude of the discrete Fourier spectrum of the noise component N(n), then determining the amplitude of the denoised signal z(n) as zero.

2. The method of signal denoising according to claim 1, wherein, The method of performing multi-layer empirical mode decomposition on a baseband signal y(n) obtained by down-converting an LFM modulated pulse signal S(n) to obtain a plurality of intrinsic mode functions comprises: determining all maxima y* (n) of the baseband signal y(n) based on a spline interpolation function max (n) corresponding to the upper envelope e max (n) of the baseband signal y(n), and min (n) corresponding to the lower envelope e min (n) of the baseband signal y(n); determining a high-frequency detail signal d(n) based on a difference between the baseband signal y(n) and an average value m(n) of upper and lower envelopes; If it is determined that the high-frequency detail signal d(n) satisfies the condition for the intrinsic mode function, the high-frequency detail signal d(n) is determined as the intrinsic mode function IMF obtained by empirical mode decomposition of the current layer i (n); determining a corresponding residual signal r(n) based on a difference between the baseband signal y(n) and the intrinsic mode function IMF i (n). If it is determined that the residual signal r(n) satisfies the end condition of the multi-layer empirical mode decomposition, all intrinsic mode functions IMFs corresponding to the residual signal r(n) are determined i (n) constitute the intrinsic mode functions.

3. The method of signal denoising according to claim 2, wherein, The method further comprises: if it is determined that the high-frequency detail signal d(n) does not satisfy an intrinsic mode function condition, then updating the baseband signal y(n) with the high-frequency detail signal d(n); determining a new high-frequency detail signal d(n) based on the updated baseband signal y(n).

4. The method for signal denoising according to claim 2, wherein, The method further comprises: if it is determined that the residual signal r(n) does not satisfy an end condition of the multi-layer empirical mode decomposition, then updating the baseband signal y(n) with the residual signal r(n); determining a new residual signal r(n) based on the updated residual signal r(n).

5. The method for signal denoising according to claim 1, wherein, The method of reconstructing a signal component s(n) and a noise component N(n) of the baseband signal y(n) based on the intrinsic mode functions and energy values of the intrinsic mode functions comprises: determining an energy value corresponding to each intrinsic mode function to construct an energy spectrum corresponding to all intrinsic mode functions; determining an intrinsic mode function corresponding to a point of energy mutation in the energy spectrum as a serial number of the intrinsic mode function, and taking the serial number as a boundary point; determining a noise component N(n) of the reconstructed baseband signal y(n) based on a sum of all intrinsic mode functions with serial numbers less than the boundary point; determining a signal component s(n) of the reconstructed baseband signal y(n) based on a sum of all intrinsic mode functions with serial numbers greater than or equal to the boundary point and a residual signal.

6. The method of signal denoising of claim 1, wherein, The method of determining a corresponding denoised signal z(n) based on amplitudes of discrete Fourier spectra of the reconstructed signal component s(n) and the reconstructed noise component N(n) comprises: determining the discrete Fourier spectrum of the reconstructed signal component s(n) and the discrete Fourier spectrum of the reconstructed noise component N(n) based on a discrete Fourier transform, respectively; determining an amplitude of the de-noised signal z(n) based on a magnitude of an amplitude of a discrete Fourier spectrum of the signal component s(n) and an amplitude of a discrete Fourier spectrum of the noise component N(n); performing inverse discrete Fourier transform on the amplitude of the de-noised signal z(n) to determine the de-noised signal z(n).

7. The method of signal denoising according to claim 6, wherein, The specific formula for performing inverse discrete Fourier transform on the amplitude of the de-noised signal z(n) to determine the de-noised signal z(n) is: Wherein, Z(n) is the amplitude of the de-noised signal z(n), N is the sequence length of z(n), n is the sequence number of the sequence of z(n), k is the signal frequency domain component, F -1 [] is the inverse discrete Fourier transform.

8. The method of signal denoising according to claim 2 or 3, wherein, The condition for the eigenmode function to be valid includes: The sum of the number of all maxima y max (n) and the number of all minima y min (n) in the whole time range corresponding to the LFM modulated pulse signal S(n) is equal to or differs by one from the number of zero crossings of the baseband signal y(n). The average value m(n) of the upper and lower envelopes is zero at any time period.

9. The method for signal denoising according to claim 2 or 4, characterized in that, The end condition of the multi-layer empirical mode decomposition is that the residual signal is a monotonic function or a maximum value of the residual signal r(n) is less than a specified threshold SD, and the specified threshold SD and the intrinsic mode function IMF i (n) one-to-one.

10. The method for signal denoising according to claim 9, wherein, the specified threshold SD and the eigenmode function IMF i (n) one-to-one, specifically the following correspondence: where h i (t) is the Hilbert transform of the intrinsic mode function IMF i (n), the range 0 ~ T is the length of the entire intrinsic mode function IMF i (n), and i is the index of the intrinsic mode function IMF i (n).

11. The method for signal denoising according to claim 1, wherein, The LFM modulated pulse signal S(n) is received by the receiver at a sampling rate f s The discrete signal obtained from the received radio frequency signal S(t), wherein the sampling rate f s is greater than the Nyquist sampling rate.

12. The method of signal denoising according to claim 2, wherein, The spline difference function is a cubic spline difference.

13. The method of signal denoising of claim 2, wherein, The average value m(n) of the upper and lower envelopes is determined by a pre-defined formula, which is: where e max (n) is the upper envelope corresponding to all maxima y* max (n) of the baseband signal y(n). min (n) is the lower envelope corresponding to all minima y* min (n) of the baseband signal y(n).

14. The method of signal denoising of claim 5, wherein, The determination of the energy value corresponding to each eigenmode function and the construction of the energy spectrum corresponding to all eigenmode functions include: The energy value of each eigenmode function is determined according to an energy formula to form a corresponding energy spectrum, and the energy formula is: L is an intrinsic mode function, IMF i (n) is a sequence length, i is an intrinsic mode function, IMF i (n) is a sequence number, E(i) is an intrinsic mode function, IMF, of sequence number i i (n) is an energy value.

15. The method for signal denoising according to claim 5, wherein, The formula for determining the noise component N(n) of the reconstructed baseband signal y(n) is: The formula for determining the signal component s(n) of the reconstructed baseband signal y(n) is: where h is the intrinsic mode function IMF corresponding to the point of energy mutation in the intrinsic mode function energy spectrum i (n) is the sequence number, M is the number of intrinsic mode functions, and r(n) is the residual signal.

16. An electronic device for signal de-noising, comprising a memory, a transceiver, and a processor; The memory is configured to store a computer program. The transceiver is configured to transceive data under the control of the processor. The processor is configured to execute the computer program in the memory and implement the steps of the signal de-noising method according to any one of claims 1 to 15.

17. An apparatus for signal denoising, the apparatus comprising: The device comprises: The decomposition module is configured to perform multi-layer empirical mode decomposition on a baseband signal y(n) obtained by down-converting an LFM modulated pulse signal S(n) to obtain a plurality of eigenmode functions; The reconstruction module is configured to reconstruct a signal component s(n) and a noise component N(n) of the baseband signal y(n) based on the eigenmode functions and the energy values of the eigenmode functions; The determination module is configured to determine a corresponding de-noised signal z(n) based on an amplitude of a discrete Fourier spectrum of the reconstructed signal component s(n) and an amplitude of a discrete Fourier spectrum of the reconstructed noise component N(n), wherein the determination includes: If the amplitude of the discrete Fourier spectrum of the signal component s(n) is greater than the amplitude of the discrete Fourier spectrum of the noise component N(n), then the difference between the two amplitudes is determined as the amplitude of the de-noised signal z(n); If the amplitude of the discrete Fourier spectrum of the signal component s(n) is less than or equal to the amplitude of the discrete Fourier spectrum of the noise component N(n), then the amplitude of the de-noised signal z(n) is determined as zero.

18. A processor-readable storage medium, comprising: The processor readable storage medium stores a computer program for causing the processor to execute the signal de-noising method according to any one of claims 1 to 15.

19. A computer program product comprising a computer program, characterized in that, The computer program, when executed by the processor, implements the steps of the signal de-noising method according to any one of claims 1 to 15.

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