A signal denoising method based on time-frequency graph order statistics

Abstract

The application discloses a signal denoising method based on time-frequency graph order statistics, and belongs to the technical field of signal processing. The signal denoising method based on time-frequency graph order statistics comprises the following steps: generating a time-frequency graph based on received signal data; estimating the maximum order statistics of the db value of the corresponding frequency signal along the time domain direction of the time-frequency graph with respect to the frequency domain, and determining the maximum order statistics as the noise upper limit at the frequency; setting a sensitive domain according to the maximum bandwidth of the target signal along the frequency domain direction of the time-frequency graph based on the noise upper limit; estimating the distribution of noise in the frequency domain based on the sensitive domain; and denoising the signal data based on the distribution of noise in the frequency domain. The signal denoising detection method based on time-frequency graph order statistics has high universality and interpretability.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and in particular relates to a signal denoising method based on time-frequency graph order statistics. Background Technology

[0002] Radio communication is widely used in almost every field requiring "communication," such as meteorology, telecommunications, military, and transportation, to transmit information such as text, voice, images, and data streams. The identification and analysis of communication signals can greatly assist in further information processing and applications, and has significant practical implications in areas such as military reconnaissance, electronic warfare, and information network security. However, after signals are encoded and sent to a wireless channel, the receiving end will inevitably experience a certain degree of noise interference if transmitted over long distances.

[0003] Because there are many types of noise, such as Gaussian noise, salt-and-pepper noise, and impulse noise, methods designed for specific types of noise may not be effective for other types. Furthermore, designing different denoising and detection algorithms for each type of noise is overly idealistic and often impossible due to cost and computational limitations. Therefore, designing a general-purpose signal denoising and detection method is a more economical and efficient solution. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a signal denoising method based on time-frequency graph order statistics.

[0005] The objective of this invention is achieved through the following technical solution: a signal denoising method based on time-frequency graph order statistics, comprising:

[0006] Generate a time-frequency diagram based on the received signal data;

[0007] Estimate the maximum order statistic of the corresponding frequency signal dB value along the time domain direction of the time-frequency plot, and determine the maximum order statistic as the noise upper limit at that frequency;

[0008] Based on the noise upper limit along the frequency domain direction of the time-frequency diagram, the sensitive domain is set according to the maximum bandwidth of the target signal;

[0009] The noise distribution in the frequency domain is estimated based on the aforementioned sensitive domain;

[0010] Denoising of signal data is performed based on the distribution of noise in the frequency domain.

[0011] Furthermore, a time-frequency diagram is generated based on the received signal data, including:

[0012] Determine the number of FFT points in the short-time Fourier transform;

[0013] The received signal data is subjected to a short-time Fourier transform to generate a time-frequency graph. Before mapping, the value of each point in the time-frequency graph is the amplitude in dB of the signal.

[0014] Furthermore, if the length of the signal data is less than a preset value, then the adjacent windows of the short-time Fourier transform overlap.

[0015] Furthermore, along the time-domain direction of the time-frequency plot, the maximum order statistic of the corresponding frequency signal dB value is estimated with respect to the frequency domain, and this maximum order statistic is determined as the noise upper limit at that frequency, including:

[0016] By dividing the frequency domain into equal intervals along the time domain, the maximum order statistics of each frequency band in multiple time domains are obtained.

[0017] The mean of the corresponding maximum order statistic is estimated using the order sampled values ​​within each time domain.

[0018] The maximum order statistic is determined as the upper limit of noise at the corresponding frequency.

[0019] Furthermore, there is overlap between adjacent sensitive domains.

[0020] Furthermore, when setting the sensitive domain according to the maximum bandwidth of the target signal along the frequency domain direction of the time-frequency diagram based on the noise upper limit, the resulting multiple sensitive domains include at least two sizes of sensitive domains.

[0021] Furthermore, based on the noise upper limit along the frequency domain direction of the time-frequency diagram, a sensitive domain is set according to the maximum bandwidth of the target signal, including:

[0022] Based on the noise upper limit along the frequency domain direction of the time-frequency graph, the sensitive domain is set according to the maximum bandwidth of the target signal and the frequency resolution of the time-frequency graph.

[0023] Furthermore, signal denoising methods based on time-frequency graph order statistics also include:

[0024] Detect the signal according to the minimum signal-to-noise ratio requirement; and / or,

[0025] Target parameters are detected based on the temporal and frequency domain resolutions of the time-frequency plot.

[0026] Furthermore, the time resolution of the time-frequency diagram is:

[0027]

[0028] In the formula, Δt is the time resolution of the time-frequency plot, l is the step size of the FFT window function, and fs is the sampling rate of the receiver;

[0029] The frequency resolution of the time-frequency graph is:

[0030]

[0031] In the formula, Δf is the frequency resolution of the time-frequency plot, fs is the sampling rate of the receiver, and N is the number of points in each frame of FFT.

[0032] Furthermore, the target parameters include one or more of the signal's center frequency, signal bandwidth, and signal start and end times.

[0033] The beneficial effects of this invention are:

[0034] (1) The signal denoising detection method based on time-frequency graph order statistics proposed in this invention has strong versatility and interpretability. The order statistics method on which it is based has strict theoretical guarantees, is not a black box system, and is robust to the distribution of noise. That is, for common noise distributions or distributions of noise dynamics that change slowly, this invention can make accurate estimates. At the same time, it supports narrowband and wideband signal detection, especially with better adaptability when the frequency band is wide.

[0035] (2) The methods used in this invention can all be processed in parallel on the time-frequency graph, resulting in high computational efficiency;

[0036] (3) The method of the present invention is highly compatible with various types of receiving devices and can be embedded in most signal processing devices to expand their functions, thus possessing strong scalability. Attached Figure Description

[0037] Figure 1 This is a flowchart of an embodiment of the signal denoising method based on time-frequency graph order statistics in this invention;

[0038] Figure 2 This is a diagram illustrating the effect of the present invention in estimating the upper limit of noise at a single frequency using order statistics;

[0039] Figure 3 This is a distribution diagram showing the noise floor estimation when the sensitive domain is set close to the maximum signal bandwidth according to the present invention;

[0040] Figure 4 This is a distribution diagram showing the estimated noise floor when the sensitive domain is set to twice the maximum signal bandwidth.

[0041] Figure 5 The original image is used to demonstrate the signal denoising detection effect of this invention.

[0042] Figure 6 This diagram illustrates the signal denoising detection effect of the present invention. Detailed Implementation

[0043] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] See Figures 1 to 6 This invention provides a signal denoising method based on time-frequency graph order statistics:

[0045] like Figure 1 As shown, a signal denoising method based on time-frequency graph order statistics includes S100 to S500.

[0046] S100. Generate a time-frequency diagram based on the received signal data.

[0047] In some embodiments, generating a time-frequency graph based on received signal data includes: determining the number of FFT points for a short-time Fourier transform; performing a short-time Fourier transform on the received signal data to generate a time-frequency graph, wherein the value of each point in the time-frequency graph before mapping is the dB value of the signal amplitude.

[0048] In some embodiments, if the length of the signal data is less than a preset value, the windows of the short-time Fourier transform can be appropriately overlapped. The size of the overlap is determined according to the actual situation, and the overlap area is less than or equal to half the number of FFT points.

[0049] S200. Estimate the maximum order statistic of the corresponding frequency signal dB value along the time domain direction of the time-frequency diagram, and determine the maximum order statistic as the noise upper limit at that frequency.

[0050] In some embodiments, the effect of estimating the noise upper limit is shown in the figure. Figure 2 As shown, Figure 2 The relative dB value is the actual dB value of the signal plus a non-negative constant (the use of the relative dB value is for the protection of the original signal data, and this processing will not have any effect on this method).

[0051] In some embodiments, the principle for estimating the maximum order statistic and noise distribution is derived as follows:

[0052] Let the distribution function of the noise be F(x), and the corresponding density function be p(x), x1,x2,…,x n For the signal amplitude sampled from the time domain in the frequency domain, the distribution of the k-th maximum order statistic satisfies:

[0053]

[0054] In the formula, Δx→0 is the expression of the limit, and Γ is the gamma function.

[0055] Specifically, when k = n, the distribution of the maximum order statistic can be obtained as follows:

[0056] p n (x)=n·(F(x)) n-1 p(x)

[0057] When the noise follows a mean of μ and a variance of σ 2 When the distribution is Gaussian, the specific distribution of the above maximum order statistic is as follows:

[0058]

[0059] The same principle applies to cases where the noise distribution follows other distributions.

[0060] Solving similar equations is relatively difficult, and estimating the parameters in the equation using maximum likelihood estimation also requires a large amount of computation. Therefore, in this embodiment, the Monte Carlo method is used to estimate the maximum order statistic of similar equations. Specifically, by dividing the frequency domain into equal intervals along the time domain, the maximum order statistic in multiple time domains under each frequency band can be obtained. Using the order sampling values ​​in each time domain, the mean of the corresponding order statistic can be estimated (here, the mean is the mean of the same order statistic in all time domains, for example, the mean estimation of the maximum order statistic; due to the presence of noise parameters, using the mean can improve the reliability of the results) or other statistics of the order statistic (regarding other statistics, statistics that meet the corresponding statistical characteristics can be estimated, but the mean estimation is simple, universal, and has low computational complexity), which is guaranteed by the law of large numbers. That is, if {X} i} Independent and identically distributed, and X i If the expected value of the distribution exists, then for any e > 0, the following equation holds:

[0061]

[0062] In the formula, P is the probability and E is the expectation.

[0063] Therefore, to ensure estimation accuracy, the number of time domains cannot be too small. The specific number of time domains is determined based on the actual situation; for example, in some embodiments, the number of time domains is greater than 50. The equation estimated using the Monte Carlo method... It is the upper limit of noise at that frequency.

[0064] S300. Based on the noise upper limit along the frequency domain direction of the time-frequency diagram, set the sensitive domain according to the maximum bandwidth of the target signal.

[0065] In some embodiments, setting a sensitive domain based on the noise upper limit along the frequency domain direction of the time-frequency map and according to the maximum bandwidth of the target signal includes: setting a sensitive domain based on the noise upper limit along the frequency domain direction of the time-frequency map and according to the maximum bandwidth of the target signal and the frequency resolution of the time-frequency map.

[0066] In this embodiment, the sensitivity field is set based on the maximum bandwidth of the target signal and the frequency resolution of the time-frequency plot. The sensitivity field is independent of the time domain and is a parameter controlling the sensitivity to the final estimated noise floor distribution. If the signal generally has a small bandwidth, for example, less than 1 MHz, but the total bandwidth is as high as hundreds of megabits, the sensitivity field can be set according to the frequency resolution corresponding to 1 MHz. Figure 2 and Figure 3 Examples of estimating noise floor distribution under different sensitivity domains are provided. The relative frequency of the axis is the frequency resolution calculated by the formula for each point, which is the true frequency plus a fixed constant multiplied by the product of the axis's corresponding coordinate and the frequency resolution (using relative frequency is for the protection of the original signal data; this processing does not affect the method). It can be seen that setting a reasonable sensitivity domain based on the maximum bandwidth of the target signal makes the estimated noise floor distribution closer to reality. Furthermore, if a smoother estimated signal noise floor distribution is required, some overlap between sensitivity domains is permissible. Also, if the signal bandwidths of multiple frequency bands of interest differ significantly, sensitivity domains of varying sizes can be set flexibly. In addition, interpolation methods can also make the noise floor distribution have a certain degree of differentiability without losing information; for example, cubic spline interpolation can be used.

[0067]

[0068] In the formula, S(x) i )=y i Let i = 0, 1, ..., n, and S be the representation of the interpolation function. This interpolation function is a piecewise function. Cubic spline interpolation is the formula described above. The subscripted S... k (x) is the piecewise interpolation function, a, b, c, and d are the coefficients of the cubic spline interpolation function, because four coefficients are needed to represent a cubic function. (x, y) are pairs of sampling points, and interpolation is performed based on these sampling points.

[0069] S400. Estimate the noise distribution in the frequency domain based on the sensitive domain.

[0070] S500. Denoise signal data based on the noise distribution in the frequency domain.

[0071] In some embodiments, the signal denoising method based on the maximum order statistic of the time-frequency graph further includes: detecting the signal according to the minimum signal-to-noise ratio requirement.

[0072] In some embodiments, the signal denoising method based on the maximum order statistic of a time-frequency diagram further comprises: detecting a target parameter based on the time resolution and frequency resolution of the time-frequency diagram.

[0073] The frequency resolution of the time-frequency diagram is:

[0074]

[0075] where Δf is the frequency resolution of the time-frequency diagram, fs is the sampling rate of the receiver, and N is the number of points of each frame of FFT.

[0076] Let the step size of the FFT window function be l. If there is no overlap between every two frames of FFT, the step size l=N; if there is overlap, l<N. The number of frames of the time-frequency diagram per second is:

[0077]

[0078] The time resolution of the time-frequency diagram is the reciprocal of the number of frames per second, that is:

[0079]

[0080] The time resolution will be used to intercept the time domain part of the effective signal.

[0081] In some embodiments, the target parameters include one or more of the center frequency of the signal, the bandwidth of the signal, and the start and end time of the signal.

[0082] Figure 5 and Figure 6 are comparison diagrams of effect diagrams of signal denoising detection performed by adopting the method of the present embodiment. It can be seen that the method of the present embodiment can well remove noise and highlight the signal, which facilitates further signal analysis.

[0083] The above description is only the preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments. The present invention can be used in various other combinations, modifications and environments, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge in the related fields. Any modifications and changes made by those skilled in the art without departing from the spirit and scope of the present invention shall fall within the protection scope of the appended claims of the present invention.

Claims

1. A signal denoising method based on time-frequency graph order statistics, characterized in that, include: Generate a time-frequency diagram based on the received signal data; Estimate the maximum order statistic of the corresponding frequency signal dB value along the time domain direction of the time-frequency plot, and determine the maximum order statistic as the noise upper limit at that frequency; Based on the noise upper limit along the frequency domain direction of the time-frequency diagram, the sensitive domain is set according to the maximum bandwidth of the target signal; The noise distribution in the frequency domain is estimated based on the aforementioned sensitive domain; Denoising signal data based on the noise distribution in the frequency domain; Estimate the maximum order statistic of the corresponding frequency signal dB value along the time domain direction of the time-frequency plot, and determine the maximum order statistic as the noise upper limit at that frequency, including: By dividing the frequency domain into equal intervals along the time domain, the maximum order statistics of each frequency band in multiple time domains are obtained. The mean of the corresponding maximum order statistic is estimated using the order sampled values ​​within each time domain. The maximum order statistic is determined as the upper limit of noise at the corresponding frequency.

2. The signal denoising method based on time-frequency graph order statistics according to claim 1, characterized in that, Generate a time-frequency diagram based on the received signal data, including: Determine the number of FFT points in the short-time Fourier transform; The received signal data is subjected to a short-time Fourier transform to generate a time-frequency graph. Before mapping, the value of each point in the time-frequency graph is the amplitude of the signal in dB.

3. A signal denoising method based on time-frequency graph order statistics according to claim 2, characterized in that, If the length of the signal data is less than a preset value, then the adjacent windows of the short-time Fourier transform overlap.

4. A signal denoising method based on time-frequency graph order statistics according to claim 1, characterized in that, There is overlap between adjacent sensitive regions.

5. A signal denoising method based on time-frequency graph order statistics according to claim 1, characterized in that, When setting the sensitive domain based on the maximum bandwidth of the target signal along the frequency domain direction of the time-frequency diagram based on the noise upper limit, the resulting multiple sensitive domains include at least two sizes of sensitive domains.

6. A signal denoising method based on time-frequency graph order statistics according to claim 1, characterized in that, Based on the noise upper limit along the frequency domain direction of the time-frequency graph, a sensitive domain is set according to the maximum bandwidth of the target signal, including: Based on the noise upper limit along the frequency domain direction of the time-frequency graph, the sensitive domain is set according to the maximum bandwidth of the target signal and the frequency resolution of the time-frequency graph.

7. A signal denoising method based on time-frequency graph order statistics according to claim 1, characterized in that, Signal denoising methods based on time-frequency graph order statistics also include: Detect the signal according to the minimum signal-to-noise ratio requirement; and / or, Target parameters are detected based on the temporal and frequency resolution of the time-frequency plot.

8. The signal denoising method based on time-frequency graph order statistics according to claim 7, characterized in that, The time resolution of the time-frequency diagram is: In the formula, Δt is the time resolution of the time-frequency plot, l is the step size of the FFT window function, and fs is the sampling rate of the receiver; The frequency resolution of the time-frequency graph is: In the formula, Δf is the frequency resolution of the time-frequency plot, fs is the sampling rate of the receiver, and N is the number of points in each frame of FFT.

9. A signal denoising method based on time-frequency graph order statistics according to claim 7, characterized in that, The target parameters include one or more of the signal's center frequency, bandwidth, and start and end times.

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