A signal detection method and system based on persistence map kapur entropy features

Abstract

The application discloses a signal detection method and system based on a persistent graph Kapur entropy feature, which comprises the following steps: firstly, calculating a power spectrum of an observation signal; then, calculating a 0-dimensional persistent graph of the power spectrum through a subset filter flow; and finally, calculating a Kapur entropy of the persistent graph as a test statistic, and comparing the test statistic with a set threshold to determine whether the observation signal contains a signal. The application firstly proposes a signal detection method through a subset filter flow, fully excavates shape information features of an inherent structure of the power spectrum, has low complexity, and can obtain better detection performance under small sample and low signal-to-noise ratio conditions, and has a better application prospect compared with existing methods.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of signal processing, and particularly relates to a signal detection method and system based on persistent graph Kapur entropy features. BACKGROUND

[0002] The detection of signals in noise is an important task in statistical signal processing, and has important applications in radar signal processing, cognitive radio spectrum sensing, biological signals, cognitive radio, deep communication and gravitational wave signal detection. At present, the existing signal detection methods mainly include a matching filter method, a deep learning method and a statistical feature detection method. The matching filter detection mainly adopts a coherent detection algorithm, and the core is a correlation operation composed of multiplication and integration, but prior information of the signal is needed. The deep learning method can automatically detect useful signals from noise under the condition that the theoretical template of the signal is lacking, but the disadvantage is that a large amount of data needs to be trained in advance, which is difficult to obtain in some scenarios. The statistical feature detection method mainly includes an energy detection method and a cyclic stationary feature detection method. For the energy detection method, the signal received at the radio frequency end is first filtered by a band-pass filter to filter out out-of-band noise and adjacent signals, then the square and integral operation of the filter output signal is performed to obtain the energy of the signal, and finally the statistical quantity is detected and judged. This method can simply and flexibly realize effective detection of the signal. However, the uncertainty of noise variance estimation can greatly reduce the energy detection performance. The cyclic stationary feature detection method judges whether the detected signal exists by checking whether the nonlinear transform spectrum of the observed signal contains a cyclic stationary frequency. Although this method has good detection performance at low signal-to-noise ratio, the calculation process is relatively complex, and different types of signals have different conditions for presenting cyclic stationary characteristics, so it is not convenient for blind detection. In recent years, a graph-based detection method has become a new detection method. The main idea of this method is to convert the signal from a time series form into a specific graph topology, and then realize the detection of the signal by detecting the complete connectivity of the graph structure. However, the processing complexity of this method is the square of the sample number, and the processing time is too long for large sample signals.

[0003] Topological signal processing is a new signal processing technology for establishing a topological space, and a graph can be regarded as a special topology. At present, the topological signal processing technology is mainly based on persistent homology transformation. The traditional processing idea is a persistent homology analysis method based on point cloud transformation. This kind of method first transforms the signal into a point cloud by a proper way, and then uses a series of nested simplexes to fit the topological change rule of the point cloud structure. The calculation complexity is high, but the flexibility and adjustability of the algorithm are good. The application obtains the persistent graph features of the time series through subset filtering, and constructs a signal detection algorithm based on the features. The operation complexity is low, and the performance is good. SUMMARY

[0004] The present application aims at the deficiencies in the prior art, and provides a signal detection method and system based on a persistence map Kapur entropy feature.

[0005] To achieve the above object, the present application adopts the following technical solutions:

[0006] A signal detection method based on a persistence map Kapur entropy feature, characterized in that it comprises the following steps:

[0007] Step 1: performing fast Fourier transform on an observation signal, and taking the square of the modulus to obtain a power spectrum of the observation signal;

[0008] Step 2: obtaining a 0-dimensional persistence map of the power spectrum of the observation signal through subset filtering;

[0009] Step 3: extracting the persistence values of each pair of points in the persistence map, and calculating the Kapur entropy of the persistence map as a detection statistic;

[0010] Step 4: performing large-value removal on the observation signal, and then performing B times resampling, calculating the Kapur entropy of the persistence map of the B times resampled data samples, and setting a threshold value according to the numerical characteristics of the Kapur entropy of the persistence map;

[0011] Step 5: judging the existence of the signal by comparing the detection statistic and the threshold value.

[0012] To optimize the above technical solutions, the following specific measures are adopted:

[0013] Further, in step 1, the observation signal is sampled at a sampling frequency f s to obtain a discrete sample set r(k) of the observation signal:

[0014] r(k) = s(k) + n(k), k = 0, 1,..., K-1

[0015] wherein n(k) is a discrete time additive Gaussian white noise sample with a mean of 0 and a variance of σ 2 , s(k) is a discrete sample of a pure signal, and K is the number of received signal samples;

[0016] The power spectrum f(m) of the observation signal is:

[0017]

[0018] Further, in step 2, the 0-dimensional persistence diagram of the power spectrum f(m) is obtained by the following way:

[0019] The power spectrum f(m) is fitted to get a continuous function f: For the function f, if its derivative f'(x) = 0, then x is a critical point; if its second derivative f"(x) ≠ 0, then x is a non-degenerate point, and the function value of the non-degenerate critical point is a local maximum or a local minimum of the function f; for each function value Consider the subset t increases continuously from -∞, if no local maximum point and local minimum point appears, then the connectivity of the subset is unchanged; if a local minimum point appears, the subset increases a connected component; if a local maximum point appears, then two connected components merge into one;

[0020] The critical points are paired according to the following rules: when a new connected component is introduced, the local minimum of this connected component represents this connected component; when a local maximum appears and there are two connected components to be paired, the local maximum is paired with the higher one of the two local minima representing the two connected components, and the other local minimum represents the connected component produced by the merging;

[0021] For two paired points (x, y), the difference f(y) - f(x) of the function is its persistence value; each paired point is mapped to (f(x), f(y)), and plotted in the two-dimensional rectangular coordinate system, thereby obtaining the persistence diagram, whose horizontal coordinate is birth, representing the function value when the connected component appears, and whose vertical coordinate is death, representing the function value when the connected component disappears.

[0022] Further, in step 3, the Kapur entropy of the persistence diagram is calculated as follows:

[0023] For the obtained persistence diagram, assuming that it has N paired points, the points of the function value mapped on the persistence diagram are {(f(x i ), f(y i ))} respectively, i = 1,..., N; the persistence value of each paired point is calculated as follows:

[0024] p i = f(y i ) - f(x i ), i = 1,..., N

[0025] And the Kapur entropy of the persistence diagram is obtained as follows:

[0026]

[0027] In the formula, Kapur entropy Adjustable parameter n>0.

[0028] Further, in the step 4, the sample value exceeding 0.8 times of the maximum value in the power spectrum f(m) of the observation signal is removed; the Bootstrap resampling is performed on the removed signal sample, and the resampling number is 5-10 times; the persistence entropy of the data sample of each resampling is calculated respectively, and the mean value thereof is calculated And the variance The threshold value is set as

[0029] Further, in the step 5, the Kapur entropy obtained in the step 3 is compared with the threshold value set in the step 4, if H PD >η, the signal does not exist in the channel; otherwise, the signal exists in the channel.

[0030] The application further provides a signal detection system based on the persistence map Kapur entropy feature, which is characterized by comprising:

[0031] A signal processing module is used for performing fast Fourier transform on the observation signal, taking the square of the modulus to obtain the power spectrum of the observation signal;

[0032] A subset filtering module is used for obtaining the 0-dimensional persistence map of the observation signal through the subset filtering of the power spectrum of the observation signal;

[0033] A statistical quantity calculation module is used for extracting the persistence value of each pair of points in the persistence map, and calculating the Kapur entropy of the persistence map as the detection statistical quantity;

[0034] A threshold setting module is used for performing the large value removal on the observation signal, then performing B times of resampling, calculating the persistence Kapur entropy of the data sample after B times of resampling, and setting the threshold value according to the numerical characteristics of the entropy;

[0035] A judgment module is used for judging the existence of the signal through the comparison between the detection statistical quantity and the threshold value.

[0036] The application further provides a computer readable storage medium, which stores a computer program, and the computer program is characterized by enabling the computer to execute the signal detection method based on the persistence map Kapur entropy feature.

[0037] The application further provides an electronic device, which is characterized by comprising a memory, a processor and a computer program stored in the memory and capable of running on the processor, and the processor executes the computer program to realize the signal detection method based on the persistence map Kapur entropy feature.

[0038] The present application fully excavates the 0-dimensional topological characteristics of power spectrum, that is, the variation law of extreme points of one-dimensional function is detected to obtain the 0-dimensional persistence graph, and the signal is further processed according to the difference of the 0-dimensional persistence graph. Moreover, the present application directly uses the Bootstrap resampling sample of the original signal sample to obtain the approximate sample mean and variance of the persistence Kapur entropy, and provides statistical basis for threshold setting, and can be applicable to the condition with poor simulation condition. The present application firstly proposes to use the subset filtering flow to perform signal detection, fully excavates the shape information characteristics of the internal structure of power spectrum itself, has low complexity, and can obtain better detection performance under the condition of small sample and low signal-to-noise ratio, and has more application prospect compared with the prior art. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 is a flow chart of a signal detection method based on the persistence graph Kapur entropy characteristics proposed by the present application.

[0040] Figure 2a and Figure 2b are the persistence graph schematic diagrams of power spectrum under the conditions of having signal and not having signal respectively.

[0041] Figure 3 represent the histograms of the power spectrum persistence graph Kapur entropy under two kinds of assumptions.

[0042] Figure 4 is a comparison diagram of the receiver operating characteristic curve (ROC) performance of the present application and the graph domain processing method when the signal-to-noise ratio is-3dB. DETAILED DESCRIPTION

[0043] The present application will be further described in detail in combination with the drawings.

[0044] In an embodiment, as shown in a signal detection method based on the persistence graph Kapur entropy characteristics, the specific process comprises the following steps: Figure 1

[0045] I. Calculate the power spectrum of the received signal.

[0046] The continuous time received signal r(t) composed of the transmission signal s(t) subjected to path loss and the additive white Gaussian noise n(t) is expressed as:

[0047] r(t) = s(t) + n(t)

[0048] wherein

[0049]

[0050] ​where ξ(δ) represents the δth information symbol sample, g(t) represents the continuous-time waveform carrying one information sample in a time duration of T0, g(t-δT0) represents the pulse corresponding to the δth symbol; at the receiving end, r(t) is sampled at a sampling frequency f s Discrete equidistant sampling is performed to obtain a discrete sample set of the observation signal (i.e. the received signal):

[0051] r(k) = s(k) + n(k), k = 0, 1,..., K-1

[0052] where n(k) is a discrete-time additive Gaussian white noise sample with mean 0 and variance σ 2 , and s(k) is a discrete sample of the pure signal;

[0053] The hypothesis testing model for signal detection is:

[0054] H0: r(k) = n(k), i.e. there is no signal in the channel;

[0055] H1: r(k) = s(k) + n(k), i.e. there is a signal in the channel.

[0056] The power spectrum of the received signal is:

[0057]

[0058] where K is the number of received signal samples and is also the number of DFT points.

[0059] II. Obtain the 0-dimensional persistence diagram of the power spectrum.

[0060] For a continuous function f obtained by fitting a power spectrum: If the derivative f'(x) = 0, then x is called a critical point (i.e. a singular point); if the second derivative f"(x) ≠ 0, then x is called a non-degenerate point. Assuming that the function f only contains non-degenerate critical points and critical values, these critical values are local maximum points or local minimum points of the function f. For each critical value x0, Consider the subset u continuously increases from -∞, if no critical value appears, then the connectivity of remains unchanged; if a local minimum point is encountered, the subset increases by one connected component; if a local maximum point is encountered, the two connected components are merged into one.

[0061] The key point pairing rules are as follows: (1) when a new connected component is introduced, the local minimum value that produces the component is called to represent the component; (2) when a local maximum value is encountered, and there are two connected components to be paired, the maximum value is paired with the higher one of the two local minimum values representing the two components, and the other minimum value represents the connected component produced by the merging. For two paired points (x, y), the difference f(y)-f(x) of the function is the persistence value thereof. Each paired point is mapped into (f(x), f(y)), and plotted in a two-dimensional rectangular coordinate system, so as to obtain a persistence diagram PD, in which the horizontal coordinate is birth, representing the function value when the connected component appears, and the vertical coordinate is death, representing the function value when the connected component disappears.

[0062] III. Calculation of detection statistic: calculation of Kapur entropy of the persistence diagram.

[0063] For the obtained persistence diagram, assuming that it has N paired points, the function values of which are mapped to points on the persistence diagram are {(f(x i ), f(y i ))}, i = 1,..., N; the persistence value of each paired point is calculated as follows:

[0064] p i = f(y i )-f(x i ), i = 1,..., N

[0065] And the Kapur entropy of the persistence diagram is obtained according to the following formula:

[0066]

[0067] In the formula, the adjustable parameter n of the Kapur entropy is greater than 0.

[0068] IV. Threshold setting.

[0069] 1) The obtained observation signal is first subjected to de-max value processing, that is, the sample value exceeding 0.8 times of the maximum value in f(m) is removed. The purpose of this is that we cannot predict in advance which hypothesis the observation signal is from, and the threshold is mainly selected according to the sample under the zero hypothesis. The de-max value processing can ensure that the sample used for calculating the threshold in the next step does not contain the signal component.

[0070] 2) The signal sample after de-max value processing is subjected to Bootstrap resampling, and the resampling number is 5-10 times. The Kapur entropy of the persistence diagram of the data sample of each resampling is calculated, and the mean value and variance thereof are calculated and represented as

[0071] 3) take the threshold as

[0072] V. Comparison decision.

[0073] The calculated Kapur entropy of PD is taken as a detection statistic, and a corresponding threshold η is set for comparison. If H PD > η, there is no signal in the channel, and H0 is determined; otherwise, there is a signal in the channel, and H1 is determined.

[0074] Figure 2a and Figure 2b is the persistence figure of the power spectrum under the signal and no-signal situation. Wherein, Figure 2a is the persistence figure of the observed signal power spectrum when there is no signal, Figure 2b is the persistence figure of the observed signal power spectrum when there is a signal.

[0075] Figure 3 The histogram represents the Kapur entropy of the power spectrum persistence figure under the two hypotheses. Wherein, the lighter column is the histogram of the Kapur entropy of the observed signal power spectrum persistence figure when there is a signal, and the darker column is the histogram of the Kapur entropy of the observed signal power spectrum persistence figure when there is a signal.

[0076] Simulation conditions: In the above figure, the signal is assumed to be a BPSK signal, the code is a 13-bit Barker code sequence, the carrier frequency is 20Mhz, the sampling frequency is 100Mhz, the sample point number is 130, the symbol width is 10 sampling intervals, the signal-to-noise ratio is -6dB, and the simulation times are 1000. If the simulation times are not specified, they are the same.

[0077] As shown in Figures 2a-2b and Figure 3 , there is a significant difference between the persistence figures converted from the observed signal power spectrum under the H0 and H1 hypotheses, and further, the Kapur entropy of the persistence figure under different hypotheses also has a large difference, which is the theoretical basis for the signal detection method.

[0078] Figure 4 is the receiver operating characteristic (ROC) performance of the method when the signal-to-noise ratio is -6dB. Other parameters in the simulation are set as described in the previous simulation conditions. As can be seen from the figure, the area under the ROC of the method is large, far from the symmetry line, and has better detection performance than existing graph domain signal detection methods.

[0079] In another embodiment, the present application proposes a signal detection system corresponding to the signal detection method based on the Kapur entropy feature of the persistence figure described above, comprising:

[0080] The signal processing module is configured to perform fast Fourier transform on the observed signal, take the square of the modulus, and obtain the power spectrum of the observed signal.

[0081] a subset filtering module, configured to obtain a 0-dimensional persistence diagram of the power spectrum of the observation signal by means of subset filtering;

[0082] a statistic calculating module, configured to extract the persistence value of each pair of points in the persistence diagram, and calculate the Kapur entropy of the persistence diagram as a detection statistic;

[0083] a threshold setting module, configured to perform large-value removal on the observation signal, and then perform B times resampling, calculate the persistence Kapur entropy of the data samples after B times resampling, and set a threshold value according to the numerical characteristics thereof;

[0084] a judging module, configured to judge the existence of the signal by comparing the detection statistic and the threshold value.

[0085] In another embodiment, the present application provides a computer readable storage medium, which stores a computer program, and the computer program causes a computer to execute the signal detection method based on the persistence diagram Kapur entropy feature as described above.

[0086] In another embodiment, the present application provides an electronic device, which comprises a memory, a processor, and a computer program stored in the memory and capable of running on the processor, and when the processor executes the computer program, a signal detection method based on the persistence diagram Kapur entropy feature is realized.

[0087] In summary, the present application introduces the persistence homology feature based on subset filtering in the topological data processing into signal detection, calculates the persistence homology by means of subset filtering of the power spectrum of the observation signal, obtains a 0-dimensional persistence diagram thereof, and further calculates the entropy feature thereof as a detection statistic. Experiments show that when the signal does not exist, the persistence diagram entropy is large, and when the signal exists, the value is small. According to this phenomenon, a suitable threshold value can be set, and the size of the 0-dimensional persistence diagram entropy of the power spectrum of the observation signal and the threshold value are compared to realize the detection of the signal. The present application fully excavates the potential structural information of the power spectrum extreme value and the shape change characteristics, and has a robust detection performance under the condition of low signal-to-noise ratio and small sample.

[0088] In embodiments disclosed herein, a computer storage medium can be a tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. Computer storage media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of computer storage media can include, but are not limited to, an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0089] The above merely describes the preferred embodiments of the present application, and the protection scope of the present application is not limited to the above-mentioned embodiments. Any technical scheme falling within the concept of the present application shall fall within the protection scope of the present application. It should be noted that, for ordinary skilled in the art, some improvements and refinements without departing from the principles of the present application shall be considered as falling within the protection scope of the present application.

Claims

1. A signal detection method based on persistent graph Kapur entropy features, characterized in that, Includes the following steps: Step 1: Perform a Fast Fourier Transform on the observed signal received at the radio frequency terminal, and take the square of its modulus to obtain the power spectrum of the observed signal. Step 2: Obtain the 0-dimensional persistence plot of the power spectrum of the observed signal by subset filtering; in Step 2, the 0-dimensional persistence plot of the power spectrum f(m) is obtained in the following way: Fitting the power spectrum f(m) yields a continuous function f: For a function f, if its derivative f′(x) = 0, then x is a key point; if its second derivative f″(x) ≠ 0, then x is a non-degenerate point. The function value corresponding to a non-degenerate key point is a local maximum or local minimum of the function f; for each function value... Consider subsets If t increases continuously from -∞, and no local maximum or local minimum point appears, then The connectivity remains unchanged; if a local minimum is encountered, the subset... Add a connected component; if a local maximum is encountered, the two connected components are merged into one. Keypoint pairing is performed according to the following rules: When a new connected component is introduced, a local minimum value of this connected component is generated to represent the connected component; when a local maximum value is encountered and there are two connected components to be paired, the local maximum value is paired with the higher of the two local minimum values ​​representing these two connected components, and the other local minimum value represents the connected component resulting from the merger. For two paired points (x, y), the difference of the function f(y) - f(x) is its persistence value; map each paired point to (f(x), f(y)) and plot it in a two-dimensional rectangular coordinate system to obtain a persistence graph, where the horizontal axis is birth, representing the function value when the connected component appears, and the vertical axis is death, representing the function value when the connected component disappears. Step 3: Extract the persistence value of each paired point in the persistence graph and calculate the Kapur entropy of the persistence graph as the detection statistic; in Step 3, the Kapur entropy of the persistence graph is calculated as follows: For the resulting persistence graph, assuming it has N paired points, the points whose function values ​​map to on the persistence graph are {(f(x)} i ),f(y i ))}, i=1,…,N; Calculate the persistence value for each paired point: p i =f(y i )-f(x i ),i=1,…,N The Kapur entropy of the persistence graph is obtained using the following formula: In the formula, Kapur entropy The adjustable parameter n>0; Step 4: Remove large values ​​from the observed signal, then perform B resampling, calculate the Kapur entropy of the persistence graph of the data samples after B resampling, and set a threshold value based on the digital characteristics of the Kapur entropy of the persistence graph. Step 5: Determine the existence of the signal by comparing the detection statistic with the threshold value.

2. The signal detection method based on persistent graph Kapur entropy features as described in claim 1, characterized in that: In step 1, the sampling frequency f s By performing discrete, equally spaced sampling, a discrete sample set r(k) of the observed signal is obtained: r(k)=s(k)+n(k),k=0,1,…,K-1 Where n(k) is a vector with a mean of 0 and a variance of σ. 2 The discrete-time additive white Gaussian noise samples, s(k) are discrete samples of the pure signal; K is the number of received signal samples; The power spectrum f(m) of the observed signal is:

3. The signal detection method based on persistent graph Kapur entropy features as described in claim 1, characterized in that: In step 4, sample values ​​exceeding 0.8 times the maximum value in the power spectrum f(m) of the observed signal are removed; the removed signal samples are resampled using Bootstrap, with 5-10 resampling cycles; the persistence entropy of the data samples from each resampled cycle is calculated, and its mean is also calculated. With variance Set the threshold value to 4. The signal detection method based on the Kapur entropy feature of a persistent graph as described in claim 3, characterized in that: In step 5, the Kapur entropy obtained in step 3 is compared with the threshold value set in step 4. If H PD If η > 1, then there is no signal in the channel; otherwise, there is a signal in the channel.

5. A signal detection system based on persistent graph Kapur entropy features, characterized in that, include: The signal processing module is used to perform a fast Fourier transform on the observed signal received at the radio frequency terminal and take the square of its modulus to obtain the power spectrum of the observed signal. A subset filtering module is used to obtain a 0-dimensional persistence map of the power spectrum of the observed signal through subset filtering; the 0-dimensional persistence map of the power spectrum f(m) is obtained in the subset filtering module in the following manner: Fitting the power spectrum f(m) yields a continuous function f: For a function f, if its derivative f′(x) = 0, then x is a key point; if its second derivative f″(x) ≠ 0, then x is a non-degenerate point. The function value corresponding to a non-degenerate key point is a local maximum or local minimum of the function f; for each function value... Consider subsets If t increases continuously from -∞, and no local maximum or local minimum point appears, then The connectivity remains unchanged; if a local minimum is encountered, the subset... Add a connected component; if a local maximum is encountered, the two connected components are merged into one. Keypoint pairing is performed according to the following rules: When a new connected component is introduced, a local minimum value of this connected component is generated to represent the connected component; when a local maximum value is encountered and there are two connected components to be paired, the local maximum value is paired with the higher of the two local minimum values ​​representing these two connected components, and the other local minimum value represents the connected component resulting from the merger. For two paired points (x, y), the difference of the function f(y) - f(x) is its persistence value; map each paired point to (f(x), f(y)) and plot it in a two-dimensional rectangular coordinate system to obtain a persistence graph, where the horizontal axis is birth, representing the function value when the connected component appears, and the vertical axis is death, representing the function value when the connected component disappears. The statistics calculation module is used to extract the persistence values ​​of each paired point in the persistence graph and calculate the Kapur entropy of the persistence graph as a detection statistic. The Kapur entropy of the persistence graph is calculated in the following manner: For the resulting persistence graph, assuming it has N paired points, the points whose function values ​​map to on the persistence graph are {(f(x)} i ),f(y i ))}, i=1,…,N; Calculate the persistence value for each paired point: p i =f(y i )-f(x i ),i=1,…,N The Kapur entropy of the persistence graph is obtained using the following formula: In the formula, Kapur entropy The adjustable parameter n>0; The threshold setting module is used to remove large values ​​from the observed signal, then perform B resampling, calculate the persistence Kapur entropy of the data sample after B resampling, and set the threshold value according to the digital characteristics of the persistence graph Kapur entropy. The judgment module is used to determine the existence of a signal by comparing the detection statistics with the threshold value.

6. A computer-readable storage medium storing a computer program, characterized in that, The computer program causes the computer to execute a signal detection method based on persistent graph Kapur entropy features as described in any one of claims 1-4.

7. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements a signal detection method based on persistent graph Kapur entropy features as described in any one of claims 1-4.

Images