Band-pass filtering and Hilbert transformation system based on FIR (Finite Impulse Response) filter

Abstract

The invention relates to the technical field of signal processing, and discloses a band-pass filtering and Hilbert transformation system based on an FIR (Finite Impulse Response) filter, which comprises an impulse response generation module, an FIR filtering module and a signal demodulation module, generating a finite long impulse response capable of performing band-pass filtering and Hilbert transformation on an input signal according to a design requirement; the FIR filtering module carries out convolution on the input signal and the finite long impulse response to obtain an analysis signal after band-pass filtering, and band-pass filtering and Hilbert transform on a time domain are realized; according to the invention, band-pass filtering and Hilbert transformation are realized only by using one filter, convolution is carried out on the input signal and the finite long impulse response, the filtered analysis signal is generated, and the analysis signal is conveniently used for signal demodulation subsequently.

Description

Technical Field

[0001] The invention relates to the technical field of signal processing, and in particular to a bandpass filtering and Hilbert transform system based on an FIR filter. Background Art

[0002] Bandpass filtering and Hilbert transform are commonly used technical means in the field of signal processing. They are widely used based on profound mathematical theory and engineering practice. Bandpass filtering means passing some frequency bands of the original signal while attenuating the frequency components of other frequency bands to an extremely low level. Hilbert transform means delaying the phase of all frequency components of the original signal by 90° without changing the amplitude of all frequency components.

[0003] In the prior art, the more common bandpass filtering and Hilbert transform are implemented through Fourier transform and inverse Fourier transform, that is, relevant calculations are performed in the frequency domain, and the output after the Hilbert transform is not an analytical signal, but a signal with the original signal phase delayed by 90°, which makes it inconvenient to use the output signal for signal demodulation. Summary of the invention

[0004] In view of this, the present invention provides a bandpass filtering and Hilbert transform system based on an FIR filter to solve the problem in the prior art that it is inconvenient to use the output signal for signal demodulation.

[0005] The present invention provides a bandpass filtering and Hilbert transform system based on an FIR filter, the system comprising: an impulse response generation module, an FIR filtering module and a signal demodulation module, wherein:

[0006] The impulse response generation module is used to obtain design requirements and generate a finite-length impulse response that can satisfy the requirements of performing bandpass filtering and Hilbert transform on the input signal in sequence according to the design requirements;

[0007] The FIR filter module is used to convolve the input signal and the finite length impulse response to obtain a bandpass filtered analytical signal, implement bandpass filtering and Hilbert transform in the time domain, and send the bandpass filtered analytical signal to the signal demodulation module;

[0008] The signal demodulation module is used to receive the bandpass filtered analytical signal sent by the FIR filtering module, and extract instantaneous parameters from the analytical signal.

[0009] The present invention designs an FIR filter that can realize bandpass filtering and Hilbert transform in the time domain, and uses only one filter to convert bandpass filtering and Hilbert transform from the frequency domain to the time domain, so that the analytical signal can be output as real-time as possible. The input signal and the finite-length impulse response are convolved to generate the filtered analytical signal, which ensures that the output signal is an analytical signal rather than a phase-delayed signal, so as to facilitate the subsequent use of the analytical signal for signal demodulation.

[0010] In an optional implementation, the impulse response generation module is used to obtain the passband frequency and generate single-sided spectrum frequency domain data in the frequency domain with an amplitude of 2 in the passband frequency band and an amplitude close to zero in other frequency bands, and the passband frequency band corresponds to the passband frequency.

[0011] The present invention performs filtering processing on the input signal according to the passband frequency, effectively removes the noise in the input signal, and improves the quality of the input signal.

[0012] In an optional implementation, the impulse response generation module is used to perform inverse Fourier transform on the frequency domain data to obtain time domain data, and determine the time domain data obtained by the inverse Fourier transform as a finite-length impulse response.

[0013] The present invention uses an impulse response generation module to perform inverse Fourier transform on frequency domain data to obtain time domain data, thereby obtaining a finite length impulse response, so as to facilitate convolution of the finite length impulse response with an input signal. At the same time, due to the stability of the impulse response, the stability of the overall signal processing process is improved.

[0014] In an optional implementation, the frequency domain data satisfies the following formula:

[0015]

[0016] Among them, α(f) is the frequency domain data, α 1 , α 2 is the passband frequency value (α 1 <α 2 ), f is the frequency value.

[0017] The present invention determines frequency domain data according to design requirements so as to generate an impulse response according to the frequency domain data.

[0018] In an optional implementation, the FIR filter module is used to convolve the input signal with the finite length impulse response to obtain an analytical signal after bandpass filtering and Hilbert transformation, wherein the passband frequency is [α 1 ,α 2 ].

[0019] In an optional implementation, the instantaneous parameters include instantaneous amplitude, instantaneous phase and instantaneous frequency.

[0020] The present invention characterizes the effective information of the analytical signal by extracting the instantaneous amplitude, instantaneous phase and instantaneous frequency from the analytical signal. The extracted instantaneous amplitude can effectively reflect the intensity change of the analytical signal, the extracted instantaneous phase can effectively and accurately locate the arrival time of the signal in the subsequent analytical signal demodulation process, and the extracted instantaneous frequency can effectively monitor the frequency deviation of the analytical signal.

[0021] In an optional implementation, the instantaneous amplitude is the modulus of the analytical signal, and the instantaneous amplitude of the analytical signal is calculated according to the following formula:

[0022]

[0023] Among them, a(n) is the time domain data, To analyze the signal, is the modulus of the analytic signal.

[0024] The present invention calculates the modulus of the analytical signal to intuitively and conveniently determine the instantaneous amplitude of the analytical signal and intuitively reflects the energy change of the analytical signal.

[0025] In an optional implementation, the instantaneous phase is the arc tangent value of the analytical signal, and the instantaneous phase of the analytical signal is calculated according to the following formula:

[0026]

[0027] Where θ(n) is the instantaneous phase of the analytical signal.

[0028] The present invention obtains the arctangent value of the analytical signal by calculating the arctangent value of the analytical signal, reflects the periodic structure and change trend of the analytical signal, and facilitates demodulation of the analytical signal.

[0029] In an optional implementation, the instantaneous frequency of the analytical signal is calculated according to the following formula:

[0030]

[0031] Where f(n) is the instantaneous frequency of the analytical signal.

[0032] The present invention calculates the instantaneous frequency of the analytical signal so that the accurate instantaneous frequency can effectively enhance the stability and robustness of the demodulation algorithm and improve the overall performance in a communication scenario with rapid changes or interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0034] Figure 1 is a schematic diagram of the overall structure of a bandpass filtering and Hilbert transform system based on an FIR filter according to an embodiment of the present invention;

[0035] Figure 2 is a schematic diagram of a finite length impulse response according to an embodiment of the present invention;

[0036] Figure 3 is a schematic diagram of an input original signal according to an embodiment of the present invention;

[0037] Figure 4 is a schematic diagram of an output analysis signal according to an embodiment of the present invention;

[0038] Figure 5 is a schematic diagram of the instantaneous amplitude of an analytical signal according to an embodiment of the present invention;

[0039] Figure 6 is a schematic diagram of the instantaneous phase of an analytical signal according to an embodiment of the present invention;

[0040] Figure 7 is a schematic diagram of analyzing the instantaneous frequency of a signal according to an embodiment of the present invention. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0042] First, the terms appearing in the present invention are explained:

[0043] FIR filter: FIR (Finite Impulse Response) filter is a filter with a finite unit impulse response. It convolves the noisy signal with the finite unit impulse response to filter out points at or outside a specific frequency. The finite unit impulse response is actually a finite number of discretized values ​​of the inverse Fourier transform of the frequency domain filter.

[0044] Bandpass filtering: refers to the ability to pass some frequency bands of the original signal while attenuating the frequency components of other frequency bands to extremely low levels. There is no ideal bandpass filter, that is, bandpass filtering cannot attenuate all frequencies outside the passband to 0, nor can it guarantee that the frequencies within the passband are not amplified or attenuated.

[0045] Hilbert transform: In a physical sense, the Hilbert transform delays the phase of all frequency components of the original signal by 90°, but does not change the amplitude of all frequency components, that is, it is orthogonal to its Hilbert transform; in terms of formula definition, the Hilbert transform of an original signal x(t) refers to its difference from the impulse response Perform convolution, that is:

[0046]

[0047] Perform Fourier transform on both sides of formula (1) to obtain formula (2):

[0048]

[0049] Taking the original signal x(t) as the real part, the signal after Hilbert transformation is As a function of the imaginary part To parse the signal:

[0050]

[0051] Performing Fourier transform on both sides of formula (4) yields formula (5):

[0052]

[0053] Therefore, the analytical signal can be used for signal demodulation to obtain the instantaneous amplitude, instantaneous phase, and instantaneous frequency, which is one of the important functions of the Hilbert transform. It can be seen from formula (5) that the analytical signal has no negative frequency component, and the impulse response of the analytical signal must be a complex signal. Therefore, the more common way to obtain the analytical signal using the Hilbert transform is in the frequency domain.

[0054] Its main defects include the following two points:

[0055] (1) The commonly used bandpass filtering and Hilbert transform methods are implemented through Fourier transform and inverse Fourier transform, that is, related calculations are performed in the frequency domain. The main defect of this method is that the time domain data can only be converted into valid frequency domain data through FFT when it has a certain length and is an integer multiple of 2. In theory, real-time bandpass filtering and Hilbert transform cannot be achieved, which leads to data transmission and display lags and a decrease in frame rate.

[0056] (2) Currently, two filters are often required to implement bandpass filtering and Hilbert transform, and the output after Hilbert transform is not an analytical signal, but only a signal with the original signal phase delayed by 90°. This is quite unfriendly for most applications that need to use analytical signals for signal demodulation.

[0057] In view of the above defects, an embodiment of the present invention provides a bandpass filtering and Hilbert transform system based on an FIR filter, including an FIR filter, which can simultaneously implement bandpass filtering and Hilbert transform in the time domain, and finally obtain an analytical signal after bandpass filtering. That is, a filter is used to implement real-time signal processing, and the output result is convenient for subsequent signal demodulation.

[0058] In this embodiment, a bandpass filtering and Hilbert transform system based on FIR filter is provided. Figure 1 As shown, the system further includes an impulse response generating module 1 , a FIR filtering module 2 and a signal demodulating module 3 .

[0059] The impulse response generation module 1 is used to obtain design requirements and generate a finite-length impulse response that can satisfy the requirements of performing bandpass filtering and Hilbert transform on the input signal in sequence according to the design requirements.

[0060] The FIR filter module 2 is used to convolve the input signal and the finite length impulse response to obtain an analytical signal after bandpass filtering, realize bandpass filtering and Hilbert transform in the time domain, and send the analytical signal after bandpass filtering to the signal demodulation module 3.

[0061] The signal demodulation module 3 is used to receive the bandpass filtered analytical signal sent by the FIR filter module 2, and extract instantaneous parameters from the analytical signal.

[0062] In the embodiment of the present invention, Figure 1 As shown, first, the impulse response generation module 1 generates a finite-length impulse response according to the design requirements. Once the finite-length impulse response is generated, it does not need to be changed. The FIR filtering module 2 convolves the input signal with the finite-length impulse response generated by the impulse response generation module 1, that is, filters, to obtain an analytical signal after bandpass filtering. The signal demodulation module 3 extracts effective information such as instantaneous parameters from the filtered analytical signal in real time.

[0063] Specifically, the impulse response generation module 1 is used to obtain the passband frequency, and generate single-sided spectrum frequency domain data in the frequency domain with an amplitude of 2 in the passband frequency band and an amplitude close to zero in other frequency bands, and the passband frequency band corresponds to the passband frequency.

[0064] In the embodiment of the present invention, the impulse response generation module 1 generates a finite length impulse response according to the design requirements. 1 , α 2]Hz(α 1 <α 2 ) as an example of bandpass filtering and Hilbert transform of the passband frequency. From the frequency domain point of view, after the input signal is bandpass filtered, a single-sided spectrum frequency domain data with an amplitude of 2 in the passband frequency band and an amplitude close to zero in other frequency bands is generated in the frequency domain. After the Hilbert transform, its spectrum becomes [α 1 , α 2 ]Hz, the amplitude becomes twice the original single-sided spectrum.

[0065] The input signal is filtered according to the passband frequency to effectively remove the noise in the input signal and improve the quality of the input signal.

[0066] That is, in the frequency domain, the input signal is multiplied by α(f), and α(f) satisfies the following formula:

[0067]

[0068] Among them, α(f) is the frequency domain data, α 1 , α 2 is the passband frequency value (α 1 <α 2 ), f is the frequency value.

[0069] The frequency domain data is determined according to the design requirements so as to generate an impulse response according to the frequency domain data.

[0070] Since frequency domain multiplication is equal to time domain convolution, the frequency domain signal α(f) is subjected to inverse Fourier transform to obtain the time domain signal α(n). The time domain signal α(n) corresponding to α(f) is the generated impulse response. According to theoretical deduction, this impulse response is a complex number, which includes a real part and an imaginary part.

[0071] The impulse response generation module is used to perform inverse Fourier transform on the frequency domain data to obtain time domain data, thereby obtaining a finite length impulse response, so that the finite length impulse response can be convolved with the input signal. At the same time, due to the stability of the impulse response, the stability of the overall signal processing process is improved.

[0072] Specifically, the instantaneous parameters include effective information such as instantaneous amplitude, instantaneous phase and instantaneous frequency.

[0073] By extracting the instantaneous amplitude, instantaneous phase and instantaneous frequency from the analytical signal to characterize the effective information of the analytical signal, the extracted instantaneous amplitude can effectively reflect the intensity change of the analytical signal, the extracted instantaneous phase can effectively and accurately locate the arrival time of the signal in the subsequent analytical signal demodulation process, and the extracted instantaneous frequency can effectively monitor the frequency deviation of the analytical signal.

[0074] The input signal x(n) is passed through the FIR filter and then the output is the analytical signal The instantaneous amplitude is the modulus of the analytical signal. The instantaneous amplitude of the analytical signal is calculated according to the following formula:

[0075]

[0076] Among them, a(n) is the time domain data, To analyze the signal, is the modulus of the analytic signal.

[0077] By calculating the modulus of the analytical signal, the instantaneous amplitude of the analytical signal can be determined intuitively and conveniently, and the energy change of the analytical signal can be intuitively reflected.

[0078] The instantaneous phase is the arc tangent value of the analytical signal. The instantaneous phase of the analytical signal is calculated according to the following formula:

[0079]

[0080] Where θ(n) is the instantaneous phase of the analytical signal.

[0081] The arc tangent value of the analytical signal is obtained by calculating the arc tangent value of the analytical signal, which reflects the periodic structure and change trend of the analytical signal, so as to facilitate the demodulation of the analytical signal.

[0082] The instantaneous frequency is the derivative of the instantaneous phase divided by 2π. The instantaneous frequency of the analytical signal is calculated as follows:

[0083]

[0084] Where f(n) is the instantaneous frequency of the analytical signal.

[0085] By calculating the instantaneous frequency of the analytical signal, the accurate instantaneous frequency can effectively enhance the stability and robustness of the demodulation algorithm and improve the overall performance in communication scenarios with rapid changes or interference.

[0086] The FIR filter-based bandpass filtering and Hilbert transform system provided in this embodiment can implement bandpass filtering and Hilbert transform in the time domain through design of an FIR filter. Only one filter is used to convert bandpass filtering and Hilbert transform from the frequency domain to the time domain, so that the analytical signal can be output as real-time as possible. The input signal and the finite-length impulse response are convolved to generate the filtered analytical signal, which ensures that the output signal is an analytical signal rather than a phase-delayed signal, so as to facilitate the subsequent use of the analytical signal for signal demodulation.

[0087] Take a specific application embodiment as an example. Figure 2As shown, taking the design of a 20th-order finite-length impulse response as an example, the asymmetry in the frequency domain caused by the design requirements of bandpass filtering and Hilbert transform results in the FIR filter being a complex response. Figure 3 As shown, Figure 3 It is the original signal of the input system, where every 2048 points are continuously collected points, and there is a phase mutation between the next cycle. Figure 4 It is the analytical signal obtained after the original signal passes through the FIR filter, that is, the analytical signal obtained after [2e5 3.5e7]Hz bandpass filtering and Hilbert transform. The real part of the analytical signal is the signal of the original signal after bandpass filtering, and the imaginary part is the signal with all frequency components of the real part delayed by 90°. Figure 5 is the instantaneous amplitude of the analytical signal obtained according to the above formula (7). Figure 6 is the instantaneous phase of the analytical signal obtained according to the above formula (8). Figure 7 is the instantaneous frequency of the analytical signal obtained according to the above formula (9).

[0088] Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations all fall within the scope of the present application.

Claims

1. A bandpass filtering and Hilbert transform system based on FIR filter, characterized in that: The system includes an impulse response generation module, a FIR filtering module and a signal demodulation module, wherein: The impulse response generation module is used to obtain design requirements and generate a finite-length impulse response that can satisfy bandpass filtering and Hilbert transform of an input signal according to the design requirements; The FIR filter module is used to convolve the input signal and the finite length impulse response to obtain a bandpass filtered analytical signal, implement bandpass filtering and Hilbert transform in the time domain, and send the bandpass filtered analytical signal to the signal demodulation module; The signal demodulation module is used to receive the bandpass filtered analytical signal sent by the FIR filtering module, and extract instantaneous parameters from the analytical signal.

2. The system according to claim 1, characterized in that The impulse response generation module is used to obtain the passband frequency and generate single-sided spectrum frequency domain data in the frequency domain with an amplitude of 2 in the passband frequency band and an amplitude close to zero in other frequency bands, and the passband frequency band corresponds to the passband frequency.

3. The system according to claim 2, characterized in that The impulse response generation module is used to perform inverse Fourier transform on frequency domain data to obtain time domain data, and determine the time domain data obtained by inverse Fourier transform as a finite-length impulse response.

4. The system according to claim 3, characterized in that The frequency domain data satisfies the following formula: Among them, α(f) is the frequency domain data, α1 and α2 are the passband frequency values ​​(α1<α2), and f is the frequency value.

5. The system according to claim 1, characterized in that The FIR filter module is used to convolve the input signal with the finite length impulse response to obtain an analytical signal after bandpass filtering and Hilbert transformation, wherein the passband frequency is [α1, α2].

6. The system according to claim 1, characterized in that The instantaneous parameters include instantaneous amplitude, instantaneous phase and instantaneous frequency.

7. The system according to claim 6, characterized in that The instantaneous amplitude is the modulus of the analytical signal, and the instantaneous amplitude of the analytical signal is calculated according to the following formula: Among them, a(n) is the time domain data, To analyze the signal, is the modulus of the analytic signal.

8. The system according to claim 7, characterized in that The instantaneous phase is the arc tangent value of the analytical signal, and the instantaneous phase of the analytical signal is calculated according to the following formula: Where θ(n) is the instantaneous phase of the analytical signal.

9. The system according to claim 8, characterized in that The instantaneous frequency of the analytical signal is calculated according to the following formula: Where f(n) is the instantaneous frequency of the analytical signal.

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