Low-sampling-rate reconstruction method and device based on limited innovation rate, and storage medium

Abstract

The invention relates to the technical field of signal processing, and discloses a low-sampling-rate reconstruction method and device based on a limited innovation rate, and a storage medium. The method comprises the following steps: acquiring an observation signal obtained by performing low-sampling-rate sampling on an original signal; the original signal is a sparse signal and meets a finite innovation rate condition; based on the sampling period of the original signal and the signal period of the original signal, inversion is carried out on the observation signal through inverse transformation, and a frequency spectrum coefficient corresponding to the observation signal is obtained; based on the annihilation filter equation set and the spectrum coefficient, determining the representation coefficient of the original signal in the finite innovation rate decomposition and the sampling time of each sampling point; performing signal reconstruction on the observation signal based on the representation coefficient, the sampling time and a signal model modeled based on a finite innovation rate condition to obtain a reconstruction signal corresponding to the observation signal; according to the method, the observation signal sampled at a low sampling rate can be reconstructed, the hardware requirement on acquisition equipment is reduced, and meanwhile, the precision and reliability of signal reconstruction can be ensured.

Description

Technical Field

[0001] The present disclosure relates to the field of signal processing technology, and in particular to a low sampling rate reconstruction method, device and storage medium based on a finite innovation rate. Background Art

[0002] Signal sampling and reconstruction is one of the core issues in modern communication and signal processing. Accurate signal sampling can effectively capture the key information of the signal, while the precise reconstruction process can restore the integrity of the original signal and avoid information loss or distortion.

[0003] Traditional sampling methods include Nyquist sampling, which is to uniformly sample the original signal x(t) with a sampling period of T to obtain samples y(nT). If x(t) is a band-limited signal, that is, the spectrum of the original signal x(t) is X(ω)=0,|ω|>ω m , then we can use T≤π / ω m The sampling period is , and the sample y(nT) is losslessly reconstructed into the original signal x(t). m is the highest cutoff frequency of the original signal x(t), T is the sampling frequency of the original signal, and n is the index of the sampling point.

[0004] For signals with high carrier frequencies such as terahertz signals, if the classic Nyquist sampling method is used for sampling, an extremely high sampling frequency is required. The requirements for sampling equipment such as ADC are extremely strict, and it is difficult to match the performance parameters of existing sampling equipment. Summary of the invention

[0005] In view of this, the present disclosure proposes a low sampling rate reconstruction method, device and storage medium based on a finite innovation rate, which can reduce the requirements on the sampling frequency and the hardware equipment of the sampling device, and at the same time improve the accuracy and reliability of signal recovery.

[0006] According to one aspect of the present disclosure, a low sampling rate reconstruction method based on a finite innovation rate is provided, the method comprising:

[0007] Acquire an observation signal obtained by sampling the original signal at a low sampling rate; wherein the original signal is a sparse signal and satisfies a finite innovation rate condition;

[0008] Based on the sampling period of the original signal and the signal period of the original signal, inverting the observed signal by using an inverse transform to obtain a frequency spectrum coefficient corresponding to the observed signal;

[0009] Based on the annihilation filter equations and the spectral coefficients, determining the representation coefficients of the original signal in the finite innovation rate decomposition and the sampling time of each sampling point;

[0010] Based on the representation coefficient, the sampling time and the signal model modeled based on the finite innovation rate condition, the observed signal is reconstructed to obtain a reconstructed signal corresponding to the observed signal.

[0011] In a possible implementation, the inverting the observed signal by using an inverse transform based on the sampling period of the original signal and the signal period of the original signal to obtain a frequency spectrum coefficient corresponding to the observed signal includes:

[0012] In the case where the signal period is a positive integer multiple of the sampling period, a discrete Fourier transform is performed on the observation signal to obtain a frequency spectrum coefficient corresponding to the observation signal.

[0013] In a possible implementation, the inverting the observed signal by using an inverse transform based on the sampling period of the original signal and the signal period of the original signal to obtain a frequency spectrum coefficient corresponding to the observed signal includes:

[0014] In the case where the ratio between the signal period and the sampling period is an irrational number, based on a pre-constructed mapping model, a reversible linear mapping is used to determine the frequency spectrum coefficient corresponding to the observation signal;

[0015] The mapping model is determined by sampling the signal model through a sampling kernel function.

[0016] In a possible implementation, the mapping model is represented by the following formula:

[0017]

[0018] Among them, y n represents the sampling point obtained by sampling the original signal x(t) at the time point nT in the observed signal, n represents the index of the sampling point, and T represents the sampling period; X[m] represents the frequency spectrum coefficient of the original signal x(t), which is used to indicate the amplitude and phase of the original signal x(t) at the frequency m, and M represents the upper limit of the frequency component; τ represents the signal period.

[0019] In a possible implementation, determining the representation coefficients of the original signal in finite innovation rate decomposition and the sampling time of each sampling point based on the annihilation filter equations and the spectrum coefficients includes:

[0020] Determining annihilation filter coefficients based on the annihilation filter equations and the spectral coefficients;

[0021] constructing a polynomial equation based on the annihilation filter coefficients and obtaining roots of the polynomial equation;

[0022] Based on the roots of the polynomial equation, the representation coefficients and the sampling time of each sampling point are determined.

[0023] In a possible implementation, the annihilation filter coefficients are determined based on the annihilation filter equation group and the spectral coefficients, which are expressed by the following formula:

[0024]

[0025] Wherein, A[m] represents the annihilation filter coefficient, m represents the index of the spectrum coefficient, m is an integer from 1 to K, and K represents the total number of sampling points in the observation signal; X[k] represents the spectrum coefficient, and k is an integer from -K+1 to K;

[0026] Accordingly, the polynomial equation constructed based on the annihilation filter coefficients is expressed by the following formula:

[0027]

[0028] Wherein, A(z) represents the polynomial representation of the annihilation filter; τ represents the signal period; t k represents the time of the kth sampling point when the original signal is sampled; A[m] represents the annihilation filter coefficient, z represents the root to be solved of the polynomial equation, z includes K, the kth root z k is the sampling time t of the kth sampling point k Mapping to complex roots in the frequency domain

[0029] Accordingly, based on the roots of the polynomial equation, the representation coefficients are determined, which are represented by the following formula:

[0030]

[0031] Wherein, X[k] represents the spectral coefficient; z k represents the root of the polynomial equation; c k represents the representation coefficient, k is an integer from 0 to K-1;

[0032] Accordingly, based on the root of the polynomial equation, the sampling time of the sampling point is determined, including:

[0033] The root z of the polynomial equation k Convert to the time domain and get the sampling time t of the kth sampling point k .

[0034] In a possible implementation, the signal model based on the representation coefficient, the sampling time and the modeling based on the finite innovation rate condition is used to reconstruct the observed signal to obtain a reconstructed signal corresponding to the observed signal, which is expressed by the following formula:

[0035]

[0036] Wherein, x(t) represents the signal value of the reconstructed signal at time t; τ represents the signal period; m represents the index of the frequency component; K represents the total number of sampling points in the observed signal; c k represents the representation coefficient of the kth sampling point; t k Indicates the sampling time of the kth sampling point.

[0037] According to another aspect of the present disclosure, a low sampling rate reconstruction device based on a finite innovation rate is provided, the device comprising:

[0038] A signal acquisition module, used to acquire an observation signal obtained by sampling the original signal at a low sampling rate; wherein the original signal is a sparse signal and satisfies a finite innovation rate condition;

[0039] A signal conversion module, used to invert the observed signal using an inverse transformation based on the sampling period of the original signal and the signal period of the original signal, so as to obtain a frequency spectrum coefficient corresponding to the observed signal;

[0040] A parameter determination module, used for determining the representation coefficient of the original signal in the finite innovation rate decomposition and the sampling time of each sampling point based on the annihilation filter equation group and the spectrum coefficient;

[0041] A signal reconstruction module is used to reconstruct the observed signal based on the representation coefficient, the sampling time and the signal model modeled based on the finite innovation rate condition to obtain a reconstructed signal corresponding to the observed signal.

[0042] According to another aspect of the present disclosure, a low sampling rate reconstruction device based on a finite innovation rate is provided, comprising: a processor; a memory for storing processor executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0043] According to another aspect of the present disclosure, a non-volatile computer-readable storage medium is provided, on which computer program instructions are stored, wherein the computer program instructions implement the above method when executed by a processor.

[0044] According to another aspect of the present disclosure, a computer program product is provided, including a computer-readable code, or a non-volatile computer-readable storage medium carrying the computer-readable code. When the computer-readable code runs in a processor of an electronic device, the processor in the electronic device executes the above method.

[0045] The observed signal is obtained by sampling the original signal at a low sampling rate; wherein the original signal is a sparse signal and satisfies the finite innovation rate condition; based on the sampling period of the original signal and the signal period of the original signal, the observed signal is inverted by inverse transformation to obtain the spectrum coefficient corresponding to the observed signal; based on the annihilation filter equation group and the spectrum coefficient, the representation coefficient of the original signal in the finite innovation rate decomposition and the sampling time of each sampling point are determined; based on the representation coefficient, sampling time and the signal model modeled based on the finite innovation rate condition, the observed signal is reconstructed to obtain the reconstructed signal corresponding to the observed signal; the observed signal sampled at a low sampling rate can be reconstructed, thereby solving the problem of high hardware requirements for the acquisition device when using the Nyquist sampling method to acquire signals with higher frequencies, and the acquisition frequency of the acquisition device can be reduced, thereby reducing the hardware requirements for the acquisition device, especially when processing terahertz signals, which can significantly improve the sampling efficiency. At the same time, by combining compressed sensing and low-rank matrix recovery technology for signal reconstruction, the accuracy and reliability of signal reconstruction can be guaranteed.

[0046] Further features and aspects of the present disclosure will become apparent from the following detailed description of exemplary embodiments with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate exemplary embodiments, features, and aspects of the disclosure and, together with the description, serve to explain the principles of the disclosure.

[0048] Figure 1 A flowchart showing a low sampling rate reconstruction method based on a limited innovation rate according to an embodiment of the present disclosure is shown;

[0049] Figure 2 A block diagram of a low sampling rate reconstruction device based on a limited innovation rate according to an embodiment of the present disclosure is shown;

[0050] Figure 3 A block diagram of a low sampling rate reconstruction device based on a finite innovation rate according to another embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0051] Various exemplary embodiments, features and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise specified.

[0052] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0053] In addition, in order to better illustrate the present disclosure, numerous specific details are given in the following specific embodiments. It should be understood by those skilled in the art that the present disclosure can also be implemented without certain specific details. In some examples, methods, means, components and circuits well known to those skilled in the art are not described in detail in order to highlight the subject matter of the present disclosure.

[0054] When using the traditional Nyquist sampling method to sample high-frequency signals (such as terahertz signals), an extremely high sampling frequency is required to achieve lossless reconstruction, which leads to high hardware requirements for sampling equipment. Therefore, in order to achieve low-speed sampling without spectral aliasing, how to go beyond the classic Nyquist sampling method and efficiently and accurately restore the signal under limited sampling frequency has become a key technical challenge in many fields such as wireless communications, medical imaging, and audio processing, which directly affects system performance and application effects.

[0055] Based on the above technical problems, the present application proposes a low sampling rate reconstruction method based on finite innovation rate. This method can reconstruct the observation signal obtained by sampling at a low sampling rate based on the finite innovation rate theory (Finite Rate of Innovation, FRI) to obtain a reconstructed signal, which not only reduces the requirements for the sampling frequency and the hardware equipment of the sampling device, but also improves the accuracy and reliability of signal recovery, especially when processing terahertz signals, it can significantly improve the sampling efficiency.

[0056] Among them, FRI is a signal processing framework used to process signals with a finite rate of change, which are usually sparse signals. FRI theory provides a method to recover signals obtained through a finite number of samples, using techniques such as compressed sensing without violating the basic principles of information theory.

[0057] Sparse signals have only a few non-zero or significant components in their representation, and usually exhibit sparsity when expressed in an appropriate transform domain. Sparse signals can be efficiently compressed and reconstructed using algorithms such as compressed sensing.

[0058] The following is a detailed introduction to the low sampling rate reconstruction method based on finite innovation rate provided by the present application.

[0059] Figure 1 The flowchart of the low sampling rate reconstruction method based on limited innovation rate according to one embodiment of the present disclosure is shown. In this embodiment, the method is described by taking the method used in an electronic device with processing capability as an example. The electronic device can be a user terminal or a server. The user terminal includes but is not limited to: a mobile phone, a computer, a tablet computer, etc. This embodiment does not limit the device type of the electronic device. Figure 1 As shown, the method includes:

[0060] Step 101, obtaining an observation signal obtained by sampling an original signal at a low sampling rate; wherein the original signal is a sparse signal and satisfies a finite innovation rate condition.

[0061] Low sampling rate sampling refers to a sampling method in which the sampling frequency is lower than the Nyquist frequency, or in other words, a sampling method in which the sampling frequency is lower than twice the highest frequency component of the original signal. At this time, the observation signal is obtained by sampling the original signal with a preset sampling period, and the sampling frequency corresponding to the sampling period is lower than the Nyquist frequency. The sampled observation signal includes K sampling points, where K is a positive integer.

[0062] In this embodiment, the original signal is a sparse signal and satisfies the finite innovation rate condition. At this time, the original signal consists of only a few non-zero components, and the changes in these components have a finite innovation rate. By capturing these sparse components, effective reconstruction can be performed at a sampling rate far below the Nyquist frequency, thereby greatly reducing the demand for high-frequency sampling hardware. The innovation rate refers to a measure of the rate at which information in a signal is updated, which indicates the number of times new information in the signal is updated per unit time. Accordingly, the original signal can be represented by the sum of a series of pulses (i.e., a sparse signal), which is represented as follows:

[0063]

[0064] Where x(t) represents the signal value of the original signal at time t; c n represents the amplitude of the nth pulse; φ represents a modulation function, which may be a raised cosine roll-off function, etc. This embodiment does not limit the type of the modulation function. n represents the time when the nth pulse occurs; T represents the sampling period of the original signal.

[0065] Since the information of the modulation function φ is known, the innovation rate of the original signal expressed in the above formula does not exceed ρ = 1 / T. When the innovation rate of the original signal does not exceed ρ = 1 / T, the original signal contains at most one new information unit in each sampling period T. The information unit refers to the smallest unit in the signal that can be sampled and reconstructed, such as a pulse. In this way, the accuracy of signal reconstruction can be guaranteed.

[0066] Optionally, the original signal can be represented by using a different modulation function φ. In this case, the original signal is represented as follows:

[0067]

[0068] Among them, x(t) represents the signal value of the original signal at time t; r represents the type of modulation function φ, c nr represents the rth modulation function φ r The amplitude of the corresponding nth pulse; t n represents the time when the nth pulse occurs; T represents the sampling period of the original signal.

[0069] In the signal reconstruction process, it is generally based on φ r Construct non-uniform spline functions and piecewise polynomial functions for reconstruction and denoising. For non-uniform spline and piecewise polynomial functions, in order to make the modulation function φ r Better adapt to the local characteristics of the signal, φ r =max(t,0) r . Where max(t,0) represents the function that takes the maximum value between t and 0. At this time, φ r It is non-zero when t is positive or zero, and zero when t is negative. Based on this, the degrees of freedom of information can be obtained as follows:

[0070]

[0071] Among them, the degree of freedom of information refers to the amount of information contained in the signal within a specific time region. x (t a ,t b ) indicates that in the time zone [t a ,t b ), the number of non-zero sample points of the original signal x. 1(·) represents the indicator function, when t n In the time zone [t a ,t b ) is 1, otherwise it is 0; t n Indicates the time when the nth pulse occurs.

[0072] The innovation rate ρ is the average rate of change of the degree of freedom of information over time. Accordingly, the innovation rate ρ can be expressed by the following formula:

[0073]

[0074] The above formula represents the average number of non-zero sample points of the signal per unit time in an infinite time range. If ρ in the above formula is a finite quantity, then the original signal satisfies the finite innovation rate condition, and the original signal x is called a finite innovation rate signal. In other words, the finite innovation rate condition means that the innovation rate of the original signal is a finite quantity.

[0075] According to the above, in this embodiment, the information of the modulation function φ is known, and when the modulation function φ includes R types, the innovation rate of the original signal does not exceed ρ = R / T. Therefore, it can be seen that the original signal in this application meets the limited innovation rate condition.

[0076] Exemplarily, the original signal is a signal with a relatively high frequency, such as a terahertz signal.

[0077] Optionally, the observation signal may be collected by the electronic device; or, it may be collected by a collection device independent of the electronic device and then sent to the electronic device. This embodiment does not limit the source of the observation signal.

[0078] Step 102: Based on the sampling period of the original signal and the signal period of the original signal, the observed signal is inverted by using an inverse transform to obtain a frequency spectrum coefficient corresponding to the observed signal.

[0079] In this embodiment, the original signal x has a periodic structure, and the signal period is τ. In the framework of finite innovation rate, the original signal can be segmented and extended with τ as the period based on the expression of the original signal x, and the following formula is obtained:

[0080]

[0081] Where x(t) represents the original signal at time t; K represents the total number of sampling points in the observed signal; c k represents the representation coefficient of the kth sampling point; t k represents the sampling time of the kth sampling point; τ represents the signal period; n represents the position of the pulse in different periods, and n is an integer. δ is the function used to represent the pulse, δ(tt k -nτ) represents the time t k Pulse at +nτ.

[0082] After that, the original signal x(t) is expanded by Fourier series to obtain the signal model of the original signal based on the finite innovation rate condition:

[0083]

[0084] Wherein, m represents the index of the frequency component.

[0085] Afterwards, if we use the sampling kernel function h B=B sinc(Bt), sampling the original signal x represented by the signal model, the representation of the observed signal can be obtained as follows:

[0086] y n = <h B (t-nT),x(t)>,n=0,…,N-1,

[0087] Where <·,·> represents the inner product operation; T represents the sampling period; the above formula represents the nth sampling value y in the observed signal n is the sampling kernel function h B The inner product of (t-nT) and the original signal x(t). Sampling kernel function h B The B in it represents the bandwidth parameter of the sampling kernel function. The bandwidth parameter of the sampling kernel function is greater than or equal to the innovation rate of the original signal, that is, B ≥ ρ. In this way, an aliasing-free sampling mechanism can be provided to ensure that the original signal avoids spectrum aliasing problems at low sampling rates, so that the original signal can be correctly sampled and reconstructed.

[0088] By converting the representation of the observed signal to the frequency domain, we can obtain a mapping model between the observed signal and the original signal, which is expressed as follows:

[0089]

[0090] Among them, y n represents the sampling point obtained by sampling the original signal x(t) at time point nT in the observed signal, n represents the index of the sampling point, and T represents the sampling period; X[m] represents the spectral coefficient of the original signal x(t), which is used to indicate the amplitude and phase of the original signal x(t) at frequency m, and M represents the upper limit of the frequency component; τ represents the signal period.

[0091] According to the above derivation process, it can be known that the mapping model is determined by sampling the signal model through the sampling kernel function.

[0092] According to the mapping model, when the signal period τ is a positive integer multiple of the sampling period T, X[m] is the observed signal y n The discrete Fourier transform of n In this case, X[m] can be calculated by discrete Fourier transform.

[0093] At this time, based on the sampling period of the original signal and the signal period of the original signal, the observed signal is inverted using an inverse transform to obtain the spectral coefficients corresponding to the observed signal, including: when the signal period is a positive integer multiple of the sampling period, the observed signal is discrete Fourier transformed to obtain the spectral coefficients corresponding to the observed signal.

[0094] When the signal period τ / sampling period T is not a rational number, according to Vandermonde's theorem, the above mapping model gives a reversible linear mapping X[m]→y n , so we can get n The value of X[m] is calculated by inverting the value of

[0095] At this time, based on the sampling period of the original signal and the signal period of the original signal, the observed signal is inverted using an inverse transform to obtain the spectral coefficients corresponding to the observed signal, including: when the ratio between the signal period and the sampling period is an irrational number, based on a pre-constructed mapping model, a reversible linear mapping is used to determine the spectral coefficients corresponding to the observed signal.

[0096] Step 103, based on the annihilation filter equations and the spectrum coefficients, determine the representation coefficients of the original signal in the finite innovation rate decomposition and the sampling time of each sampling point.

[0097] Annihilation filter is a filter used to process sparse signals. Annihilation filter can eliminate certain specific frequency components in the signal, thereby simplifying the expression of the signal. Annihilation filter can help restore the key information of the signal at a low sampling rate by filtering out unimportant frequency components.

[0098] In one example, based on the annihilation filter equation group and the spectral coefficients, the representation coefficients of the original signal in the finite innovation rate decomposition and the sampling time of each sampling point are determined, including: determining the annihilation filter coefficients based on the annihilation filter equation group and the spectral coefficients; constructing a polynomial equation based on the annihilation filter coefficients to obtain the roots of the polynomial equation; determining the representation coefficients and the sampling time of each sampling point based on the roots of the polynomial equation.

[0099] Among them, based on the annihilation filter equation group and the spectrum coefficient, the annihilation filter coefficient is determined and expressed by the following formula:

[0100]

[0101] Where A[m] represents the annihilation filter coefficient, K represents the total number of sampling points in the observed signal; X[m] represents the spectral coefficient, m represents the index of the spectral coefficient, and m is an integer from 1 to K. X[k] is the spectral coefficient of the discrete Fourier transform of the original signal x(t), which represents the original signal at frequency The spectral component at , k is an integer from -K+1 to K.

[0102] Accordingly, a polynomial equation is constructed based on the annihilation filter coefficients, which is expressed as follows:

[0103]

[0104] Where A(z) represents the polynomial representation of the annihilation filter; τ represents the signal period; t k represents the time of the kth sampling point when sampling the original signal; A[m] represents the annihilation filter coefficient, z represents the root of the polynomial equation to be solved, z includes K, the kth root z k is the sampling time t of the kth sampling point k Mapping to complex roots in the frequency domain A[0] is always equal to 1.

[0105] Accordingly, based on the roots of the polynomial equation, the expression coefficients are determined and expressed by the following formula:

[0106]

[0107] Where X[k] represents the spectral coefficient; z k represents the root of a polynomial equation; c k represents the coefficient, and k is an integer from 0 to K-1.

[0108] Accordingly, based on the root of the polynomial equation, the sampling time of the sampling point is determined, including: k Convert to the time domain and get the sampling time t of the kth sampling point k . k is an integer from 0 to K-1.

[0109] For example, since for any root z k correspond Therefore, the frequency Accordingly,

[0110] Step 104 , based on the representation coefficient, the sampling time and the signal model modeled based on the finite innovation rate condition, the observed signal is reconstructed to obtain a reconstructed signal corresponding to the observed signal.

[0111] Since the expression coefficient c k and sampling time t k It is known that, therefore, the representation coefficients and sampling time can be substituted into the above signal model to obtain the reconstructed signal. Exemplarily, the meanings of the signal model and parameters in the reconstruction process are as follows:

[0112]

[0113] Where x(t) represents the signal value of the reconstructed signal at time t; τ represents the signal period; m represents the index of the frequency component; K represents the total number of sampling points in the observed signal; c k represents the representation coefficient of the kth sampling point; t k Indicates the sampling time of the kth sampling point.

[0114] In summary, the low sampling rate reconstruction method based on finite new interest rate provided in this embodiment is obtained by sampling the original signal at a low sampling rate to obtain the observed signal; wherein the original signal is a sparse signal and satisfies the finite new interest rate condition; based on the sampling period of the original signal and the signal period of the original signal, the observed signal is inverted by inverse transformation to obtain the spectrum coefficient corresponding to the observed signal; based on the annihilation filter equation group and the spectrum coefficient, the representation coefficient of the original signal in the finite new interest rate decomposition and the sampling time of each sampling point are determined; based on the representation coefficient, the sampling time and the signal model modeled based on the finite new interest rate condition, the observed signal is reconstructed to obtain the reconstructed signal corresponding to the observed signal; the observed signal sampled at a low sampling rate can be reconstructed, thereby solving the problem of high hardware requirements for the acquisition device when using the Nyquist sampling method to acquire signals with higher frequencies, and the acquisition frequency of the acquisition device can be reduced, thereby reducing the hardware requirements for the acquisition device, especially when processing terahertz signals, which can significantly improve the sampling efficiency. At the same time, by combining compressed sensing and low-rank matrix recovery technology for signal reconstruction, the accuracy and reliability of signal reconstruction can be guaranteed.

[0115] Figure 2 A block diagram of a low sampling rate reconstruction device based on a finite innovation rate according to an embodiment of the present disclosure is shown. The device comprises the following modules: a signal acquisition module 210 , a signal transformation module 220 , a parameter determination module 230 and a signal reconstruction module 240 .

[0116] The signal acquisition module 210 is used to acquire an observation signal obtained by sampling the original signal at a low sampling rate; wherein the original signal is a sparse signal and satisfies a finite innovation rate condition;

[0117] A signal conversion module 220, configured to invert the observed signal using an inverse transformation based on the sampling period of the original signal and the signal period of the original signal, to obtain a frequency spectrum coefficient corresponding to the observed signal;

[0118] A parameter determination module 230, for determining the representation coefficients of the original signal in finite innovation rate decomposition and the sampling time of each sampling point based on the annihilation filter equations and the spectral coefficients;

[0119] The signal reconstruction module 240 is used to reconstruct the observed signal based on the representation coefficient, the sampling time and the signal model modeled based on the finite innovation rate condition to obtain a reconstructed signal corresponding to the observed signal.

[0120] In a possible implementation, the signal conversion module 220 is used to:

[0121] In the case where the signal period is a positive integer multiple of the sampling period, a discrete Fourier transform is performed on the observation signal to obtain a frequency spectrum coefficient corresponding to the observation signal.

[0122] In a possible implementation, the signal conversion module 220 is used to:

[0123] In the case where the ratio between the signal period and the sampling period is an irrational number, based on a pre-constructed mapping model, a reversible linear mapping is used to determine the frequency spectrum coefficient corresponding to the observation signal;

[0124] The mapping model is determined by sampling the signal model through a sampling kernel function.

[0125] In a possible implementation, the mapping model is represented by the following formula:

[0126]

[0127] Among them, y n represents the sampling point obtained by sampling the original signal x(t) at the time point nT in the observed signal, n represents the index of the sampling point, and T represents the sampling period; X[m] represents the frequency spectrum coefficient of the original signal x(t), which is used to indicate the amplitude and phase of the original signal x(t) at the frequency m, and M represents the upper limit of the frequency component; τ represents the signal period.

[0128] In a possible implementation, the parameter determination module 230 is used to:

[0129] Determining annihilation filter coefficients based on the annihilation filter equations and the spectral coefficients;

[0130] constructing a polynomial equation based on the annihilation filter coefficients and obtaining roots of the polynomial equation;

[0131] Based on the roots of the polynomial equation, the representation coefficients and the sampling time of each sampling point are determined.

[0132] In a possible implementation, the annihilation filter coefficients are determined based on the annihilation filter equation group and the spectral coefficients, which are expressed by the following formula:

[0133]

[0134] Wherein, A[m] represents the annihilation filter coefficient, m represents the index of the spectrum coefficient, m is an integer from 1 to K, and K represents the total number of sampling points in the observation signal; X[k] represents the spectrum coefficient, and k is an integer from -K+1 to K;

[0135] Accordingly, the polynomial equation constructed based on the annihilation filter coefficients is expressed by the following formula:

[0136]

[0137] Wherein, A(z) represents the polynomial representation of the annihilation filter; τ represents the signal period; t k represents the time of the kth sampling point when the original signal is sampled; A[m] represents the annihilation filter coefficient, z represents the root to be solved of the polynomial equation, z includes K, the kth root z k is the sampling time t of the kth sampling point k Mapping to complex roots in the frequency domain

[0138] Accordingly, based on the roots of the polynomial equation, the representation coefficients are determined, which are represented by the following formula:

[0139]

[0140] Wherein, X[k] represents the spectral coefficient; z k represents the root of the polynomial equation; c k represents the representation coefficient, k is an integer from 0 to K-1;

[0141] Accordingly, based on the root of the polynomial equation, the sampling time of the sampling point is determined, including:

[0142] The root z of the polynomial equation k Convert to the time domain and get the sampling time t of the kth sampling point k .

[0143] In a possible implementation, the signal reconstruction performed by the signal reconstruction module is expressed by the following formula:

[0144]

[0145] Wherein, x(t) represents the signal value of the reconstructed signal at time t; τ represents the signal period; m represents the index of the frequency component; K represents the total number of sampling points in the observed signal; c k represents the representation coefficient of the kth sampling point; t k Indicates the sampling time of the kth sampling point.

[0146] For relevant details, please refer to the above method embodiment.

[0147] In some embodiments, the functions or modules included in the device provided by the embodiments of the present disclosure can be used to execute the method described in the above method embodiments. The specific implementation can refer to the description of the above method embodiments, and for the sake of brevity, it will not be repeated here.

[0148] The embodiment of the present disclosure also provides a computer-readable storage medium on which computer program instructions are stored, and the computer program instructions implement the above method when executed by a processor. The computer-readable storage medium can be a volatile or non-volatile computer-readable storage medium.

[0149] An embodiment of the present disclosure further proposes an electronic device, comprising: a processor; and a memory for storing instructions executable by the processor; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0150] The embodiments of the present disclosure also provide a computer program product, including a computer-readable code, or a non-volatile computer-readable storage medium carrying the computer-readable code. When the computer-readable code runs in a processor of an electronic device, the processor in the electronic device executes the above method.

[0151] Figure 3 1 is a block diagram of a low sampling rate reconstruction apparatus 1900 based on a limited innovation rate according to an exemplary embodiment. For example, the apparatus 1900 may be provided as a server or a terminal device. Figure 3 , the apparatus 1900 includes a processing component 1922, which further includes one or more processors, and a memory resource represented by a memory 1932 for storing instructions, such as an application, that can be executed by the processing component 1922. The application stored in the memory 1932 may include one or more modules, each corresponding to a set of instructions. In addition, the processing component 1922 is configured to execute instructions to perform the above method.

[0152] The device 1900 may also include a power supply component 1926 configured to perform power management of the device 1900, a wired or wireless network interface 1950 configured to connect the device 1900 to a network, and an input / output interface 1958 (I / O interface). The device 1900 may operate based on an operating system stored in the memory 1932, such as Windows Server 2000. TM , MacOS X TM , Unix TM ,Linux TM , FreeBSD TM or similar.

[0153] In an exemplary embodiment, a non-volatile computer-readable storage medium is also provided, such as a memory 1932 including computer program instructions, which can be executed by the processing component 1922 of the device 1900 to perform the above method.

[0154] The embodiments of the present disclosure have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A low sampling rate reconstruction method based on a finite innovation rate, characterized in that: The method comprises: Acquire an observation signal obtained by sampling the original signal at a low sampling rate; wherein the original signal is a sparse signal and satisfies a finite innovation rate condition; Based on the sampling period of the original signal and the signal period of the original signal, inverting the observed signal by using an inverse transform to obtain a frequency spectrum coefficient corresponding to the observed signal; Based on the annihilation filter equations and the spectral coefficients, determining the representation coefficients of the original signal in the finite innovation rate decomposition and the sampling time of each sampling point; Based on the representation coefficient, the sampling time and the signal model modeled based on the finite innovation rate condition, the observed signal is reconstructed to obtain a reconstructed signal corresponding to the observed signal.

2. The method according to claim 1, characterized in that The inverting the observed signal by using an inverse transform based on the sampling period of the original signal and the signal period of the original signal to obtain a frequency spectrum coefficient corresponding to the observed signal includes: In the case where the signal period is a positive integer multiple of the sampling period, a discrete Fourier transform is performed on the observation signal to obtain a frequency spectrum coefficient corresponding to the observation signal.

3. The method according to claim 1, characterized in that The inverting the observed signal by using an inverse transform based on the sampling period of the original signal and the signal period of the original signal to obtain a frequency spectrum coefficient corresponding to the observed signal includes: In the case where the ratio between the signal period and the sampling period is an irrational number, based on a pre-constructed mapping model, a reversible linear mapping is used to determine the frequency spectrum coefficient corresponding to the observation signal; The mapping model is determined by sampling the signal model through a sampling kernel function.

4. The method according to claim 3, characterized in that The mapping model is expressed by the following formula: Among them, y n represents the sampling point obtained by sampling the original signal x(t) at the time point nT in the observed signal, n represents the index of the sampling point, and T represents the sampling period; X[m] represents the frequency spectrum coefficient of the original signal x(t), which is used to indicate the amplitude and phase of the original signal x(t) at the frequency m, and M represents the upper limit of the frequency component; τ represents the signal period.

5. The method according to claim 1, characterized in that The step of determining the representation coefficient of the original signal in the finite innovation rate decomposition and the sampling time of each sampling point based on the annihilation filter equation group and the spectrum coefficients comprises: Determining annihilation filter coefficients based on the annihilation filter equations and the spectral coefficients; constructing a polynomial equation based on the annihilation filter coefficients and obtaining roots of the polynomial equation; Based on the roots of the polynomial equation, the representation coefficients and the sampling time of each sampling point are determined.

6. The method according to claim 5, characterized in that The annihilation filter coefficients are determined based on the annihilation filter equations and the spectral coefficients, which are expressed by the following formula: Wherein, A[m] represents the annihilation filter coefficient, m represents the index of the spectrum coefficient, m is an integer from 1 to K, and K represents the total number of sampling points in the observation signal; X[k] represents the spectrum coefficient, and k is an integer from -K+1 to K; Accordingly, the polynomial equation constructed based on the annihilation filter coefficients is expressed by the following formula: Wherein, A(z) represents the polynomial representation of the annihilation filter; τ represents the signal period; t k represents the time of the kth sampling point when the original signal is sampled; A[m] represents the annihilation filter coefficient, z represents the root to be solved of the polynomial equation, z includes K, the kth root z k is the sampling time t of the kth sampling point k Mapping to complex roots in the frequency domain Accordingly, based on the roots of the polynomial equation, the representation coefficients are determined, which are represented by the following formula: Wherein, X[k] represents the spectral coefficient; z k represents the root of the polynomial equation; c k represents the representation coefficient, k is an integer from 0 to K-1; Accordingly, based on the root of the polynomial equation, the sampling time of the sampling point is determined, including: The root z of the polynomial equation k Convert to the time domain and get the sampling time t of the kth sampling point k .

7. The method according to any one of claims 1 to 6, characterized in that: The signal model based on the representation coefficient, the sampling time and the finite innovation rate condition is used to reconstruct the observed signal to obtain a reconstructed signal corresponding to the observed signal, which is represented by the following formula: Wherein, x(t) represents the signal value of the reconstructed signal at time t; τ represents the signal period; m represents the index of the frequency component; K represents the total number of sampling points in the observed signal; c k represents the representation coefficient of the kth sampling point; t k Indicates the sampling time of the kth sampling point.

8. A low sampling rate reconstruction device based on a finite innovation rate, characterized in that: The device comprises: A signal acquisition module, used to acquire an observation signal obtained by sampling the original signal at a low sampling rate; wherein the original signal is a sparse signal and satisfies a finite innovation rate condition; A signal conversion module, used to invert the observed signal using an inverse transformation based on the sampling period of the original signal and the signal period of the original signal, so as to obtain a frequency spectrum coefficient corresponding to the observed signal; A parameter determination module, used for determining the representation coefficient of the original signal in the finite innovation rate decomposition and the sampling time of each sampling point based on the annihilation filter equation group and the spectrum coefficient; A signal reconstruction module is used to reconstruct the observed signal based on the representation coefficient, the sampling time and the signal model modeled based on the finite innovation rate condition to obtain a reconstructed signal corresponding to the observed signal.

9. A low sampling rate reconstruction device based on a finite innovation rate, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to implement the method described in any one of claims 1 to 8 when executing the instructions stored in the memory.

10. A non-volatile computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 8 is implemented.

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