A method and apparatus for extracting nonlinear features of a sound signal

Abstract

This invention discloses a method and apparatus for nonlinear feature extraction of sound signals, belonging to the field of signal processing technology. The method includes: obtaining the time spectrum of the sound signal through short-time Fourier transform; obtaining the total number of instantaneous frequencies based on the time spectrum and setting it as the total number of iterations; iteratively extracting features from the sound signal until the total number of iterations is completed; each iteration includes: sequentially performing demodulation and noise reduction, and synchronous spline kernel wavelet extraction transform to obtain a corresponding instantaneous frequency trajectory; and synthesizing multiple instantaneous frequency trajectories into a time-frequency representation result as the nonlinear feature extraction result. This solves the problem that existing methods struggle to achieve a balance between noise reduction and feature fidelity, affecting the accuracy and reliability of time-frequency analysis.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a method and apparatus for nonlinear feature extraction of sound signals. Background Technology

[0002] Time-frequency feature extraction techniques, a core tool for processing non-stationary sound signals, are widely used in fields such as speech signal processing, mechanical fault diagnosis, and biomedical signal processing. However, for complex real-world sound signals exhibiting strong noise backgrounds, multi-component coupling, and nonlinear frequency modulation characteristics, such as equipment noise, low signal-to-noise ratio speech, and bioacoustic signals, mainstream time-frequency feature extraction methods struggle to accurately and effectively extract nonlinear features.

[0003] First, traditional linear time-frequency feature extraction methods, such as Short-time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT), and their redistribution enhancement methods, such as Synchrosqueezing Transform (SST) and Synchroextracting Transform (SET), suffer from fundamental limitations such as insufficient time-frequency resolution, energy diffusion, and feature ambiguity when processing signals with nonlinear frequency modulation characteristics. They are unable to accurately characterize the complex time-varying trajectory of instantaneous frequencies.

[0004] Secondly, parameterized time-frequency feature extraction methods developed to improve energy concentration, such as General Linear Chirplet Wavelet Transform (GLCWT) and Adaptive Linear Chirplet Wavelet Transform (ALCWT), can better match frequency change trends through parameterized kernel functions. However, their models are mostly based on linear or piecewise linear assumptions. When dealing with complex sound signals that are highly nonlinear or whose frequency change patterns are unknown, these methods rely on linear or piecewise linear frequency models, resulting in limited matching accuracy of their parameterized models. This makes it difficult to achieve globally optimal energy convergence, leading to suboptimal global energy convergence and feature distortion.

[0005] Finally, in high-noise environments, existing noise reduction and weak feature extraction techniques based on signal decomposition or time-frequency filtering struggle to achieve a balance between noise reduction and feature fidelity when the time-frequency distributions of noise and target signals severely overlap. This leads to the distortion or loss of weak nonlinear features during extraction, resulting in a significant reduction in the accuracy and reliability of subsequent time-frequency analysis. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and apparatus for nonlinear feature extraction of sound signals, which solves the problem that existing methods are difficult to balance between noise reduction and feature fidelity, thus affecting the accuracy and reliability of time-frequency analysis.

[0007] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution:

[0008] In a first aspect, the present invention provides a method for nonlinear feature extraction of sound signals, comprising:

[0009] Acquire non-stationary sound signals to be processed;

[0010] The time spectrum of the non-stationary sound signal is obtained by short-time Fourier transform. The total number of instantaneous frequencies of the non-stationary sound signal is obtained based on the time spectrum, and the total number of instantaneous frequencies is set as the total number of iterations of the nonlinear feature extraction method of the sound signal.

[0011] The non-stationary sound signal is iteratively extracted until the total number of iterations is completed, resulting in multiple instantaneous frequency trajectories. Each iteration includes demodulation and noise reduction of the non-stationary sound signal and synchronous spline kernel wavelet extraction and transformation to obtain a corresponding instantaneous frequency trajectory.

[0012] The time-frequency representation of multiple instantaneous frequency trajectories is synthesized and used as the nonlinear feature extraction result corresponding to the non-stationary sound signal to be processed.

[0013] The aforementioned method for extracting nonlinear features from audio signals, wherein obtaining the time spectrum of a non-stationary audio signal through a short-time Fourier transform and acquiring the total number of instantaneous frequencies present in the non-stationary audio signal based on the time spectrum, includes: performing a short-time Fourier transform on the non-stationary audio signal to obtain its time spectrum, calculating its amplitude spectrum based on the time spectrum, and extracting the fundamental frequency as a reference instantaneous frequency from the amplitude spectrum; estimating the instantaneous frequencies of the remaining harmonics in the time spectrum based on the reference instantaneous frequency, harmonic theory assumptions, and a preset frequency limit; the preset frequency limit is either a Nyquist frequency limit or a preset frequency threshold limit, wherein the Nyquist frequency limit means that the frequency of the harmonic does not exceed half of the sampling frequency, and the preset frequency threshold means that the frequency of the harmonic does not exceed a preset frequency threshold; and merging the reference instantaneous frequency and the instantaneous frequencies of the remaining harmonics that satisfy the preset frequency limit to obtain the total number of instantaneous frequencies of the non-stationary audio signal in the time spectrum.

[0014] The aforementioned method for extracting nonlinear features of audio signals includes demodulation and noise reduction, which comprises: modeling the non-stationary audio signal as a superposition of multiple non-stationary signal components and noise components; selecting one non-stationary signal component from the multiple non-stationary signal components and performing carrier demodulation transformation to convert it into a demodulated non-stationary signal component; extracting the demodulated non-stationary signal component at the optimal carrier frequency that meets the bandpass filtering target through bandpass filtering; and restoring the original non-stationary signal component from the filtered demodulated non-stationary signal component through carrier reconstruction to obtain the denoised non-stationary signal component of the current iteration.

[0015] The aforementioned nonlinear feature extraction method for audio signals performs synchronous spline kernel wavelet extraction and transformation on the non-stationary signal component of the current iteration to obtain a corresponding instantaneous frequency trajectory. This includes: performing time-frequency transformation on the non-stationary signal component of the current iteration to obtain synchronous spline kernel wavelet extraction and transformation coefficients at each frequency at the current moment; performing peak detection on the amplitude of the synchronous spline kernel wavelet extraction and transformation coefficients at each frequency at the current moment, and using the frequency corresponding to the peak value of the amplitude as the instantaneous frequency estimate at the current moment; and combining the instantaneous frequency estimates at each moment in chronological order to obtain the instantaneous frequency trajectory corresponding to the non-stationary signal component of the current iteration.

[0016] The aforementioned method for nonlinear feature extraction of sound signals, wherein the synchronous spline kernel wavelet extraction transform is based on the spline kernel frequency modulated wavelet transform, by adding a synchronous extraction transform and constructing a spline kernel synchronous extraction operator. After matching demodulating the signal with nonlinear characteristics, the synchronous spline kernel wavelet extraction transform coefficients of the time-frequency ridge position are directly extracted using the spline kernel synchronous extraction operator.

[0017] The aforementioned nonlinear feature extraction method for sound signals, at time t, has an instantaneous angular frequency. The formula for calculating the transform coefficients extracted by the synchronous spline kernel wavelet is as follows: ,

[0018] In the formula, , This represents the frequency rotation operator constructed from spline kernels. This represents the frequency shift operator constructed from spline kernels. It's a newly designed window function. Represents the time variable of integration. Indicates at time The first noise reduction A non-stationary signal component, This represents an exponential function with the natural constant e as its base. Represents the imaginary unit; This indicates the spline kernel synchronous extraction operator;

[0019] Newly designed window functions The calculation formula is:

[0020] ,

[0021] In the formula, Represents the old window function; Indicates at time Frequency rotation operator constructed from spline kernels; Indicates at time Frequency shift operator constructed from spline kernel; spline kernel frequency-modulated wavelet transform constructs frequency rotation operator and frequency shift operator by fitting instantaneous frequency trajectory with polynomial.

[0022] The aforementioned nonlinear feature extraction method for sound signals, at time t, has an instantaneous angular frequency. spline kernel synchronous extraction operator The calculation formula is:

[0023] ,

[0024] In the formula, This indicates taking the real part of a complex number; Indicates the preset discrete frequency interval; represents an imaginary number; , It is a newly designed window function Partial derivative with respect to time.

[0025] The aforementioned nonlinear feature extraction method for sound signals updates the spline kernel parameters of the frequency rotation operator and the frequency shift operator with the instantaneous frequency trajectory corresponding to the denoised non-stationary signal component of the current iteration after completing the current iteration. This includes: fitting the frequency change on each spline interval with the instantaneous frequency trajectory corresponding to the denoised non-stationary signal component of the current iteration, and using the spline coefficients of each order polynomial and the complex constants in the spline interval as new spline kernel parameters.

[0026] The aforementioned nonlinear feature extraction method for sound signals, after completing the current iteration, also includes:

[0027] After separating the instantaneous frequency trajectory extracted in the current iteration from the non-stationary sound signal, the remaining part is used as the updated non-stationary sound signal. The updated non-stationary sound signal is then used for the next iteration extraction until the total number of iterations is completed.

[0028] Secondly, the present invention provides a nonlinear feature extraction device for sound signals, comprising: a signal acquisition module, a preprocessing module, a feature extraction module, and an output module;

[0029] The signal acquisition module is used to: acquire non-stationary sound signals to be processed;

[0030] The preprocessing module is used to: obtain the time spectrum of the non-stationary sound signal through short-time Fourier transform, obtain the total number of instantaneous frequencies of the non-stationary sound signal based on the time spectrum, and set the total number of instantaneous frequencies as the total number of iterations of the nonlinear feature extraction method of the sound signal;

[0031] The feature extraction module is used to: iteratively extract non-stationary sound signals until the total number of iterations is completed, and obtain multiple instantaneous frequency trajectories; each iteration includes: demodulating and denoising the non-stationary sound signals and performing synchronous spline kernel wavelet extraction transformation to obtain a corresponding instantaneous frequency trajectory; the synchronous spline kernel wavelet extraction transformation gathers the dispersed time-frequency energy into time-frequency ridges and performs nonlinear feature extraction;

[0032] The output module is used to synthesize a time-frequency representation of multiple instantaneous frequency trajectories as the nonlinear feature extraction result corresponding to the non-stationary sound signal to be processed.

[0033] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0034] The nonlinear feature extraction method for sound signals of this invention separates and processes the non-stationary signal components in the non-stationary sound signal. In each iteration, it first demodulates and reduces noise to eliminate the influence of noise, and then performs synchronous spline kernel wavelet extraction and transformation to gather the dispersed time-frequency energy into a time-frequency ridge and perform nonlinear feature extraction to obtain a high-resolution instantaneous frequency trajectory. Finally, after completing the total number of iterations, the instantaneous frequency trajectories output by all iterations are synthesized into a time-frequency representation result. This method takes into account both noise reduction and nonlinear feature extraction, and solves the problem that existing methods are difficult to balance between noise reduction and feature fidelity, which affects the accuracy and reliability of time-frequency analysis.

[0035] Specifically, it includes:

[0036] The nonlinear feature extraction method for sound signals proposed in this invention designs a synchronous spline kernel wavelet extract transform (SSCET). Based on the spline kernel frequency modulated wavelet transform (SCT), SSCET adds a synchronous extraction transform (SET) and constructs a spline kernel synchronous extraction operator (SSEO). SSCET combines the nonlinear feature extraction capability of SCT with the energy concentration characteristics of SET. The spline kernel synchronous extraction operator SSEO selects and retains only those points located on the theoretically calculated ideal time-frequency trajectory, i.e., frequency points near the time-frequency ridge, on the time-frequency plane generated by the spline kernel, thereby improving the time-frequency energy concentration and the estimation accuracy of instantaneous frequency in non-stationary sound signals.

[0037] The proposed nonlinear feature extraction method for sound signals employs a unique nested dual-iteration mechanism. In the current iteration, the outer iteration first performs demodulation-based denoising to separate the non-stationary signal components of the entire sound signal. A denoised non-stationary signal component is then selected and input into the synchronous spline kernel wavelet transform for the current iteration's inner iteration. The inner iteration outputs the instantaneous frequency trajectory corresponding to this denoised non-stationary signal component. This instantaneous frequency trajectory is then separated from the original non-stationary sound signal, and the next outer iteration selects the next denoised non-stationary signal component for input into the synchronous spline kernel wavelet transform for the next inner iteration. This external and inner iteration cycle is repeated, gradually separating, denoising, and sharpening the instantaneous frequency trajectory of the target non-stationary signal component. Finally, all instantaneous frequency trajectories are recursively obtained, forming a complete time-frequency representation of the non-stationary sound signal. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating a nonlinear feature extraction method for sound signals according to Embodiment 1 of the present invention;

[0039] Figure 2 These are schematic diagrams of the time waveform and Fourier spectrum of the male voice data collected in Embodiment 1 of the present invention.

[0040] Figure 3 This is a schematic diagram of the time-frequency representation result obtained by estimating the collected male voice data using the short-time Fourier transform of Embodiment 1 of the present invention;

[0041] Figure 4 This is a schematic diagram of the time-frequency representation result obtained by estimating the collected male voice data using the nonlinear feature extraction method of the sound signal in Embodiment 1 of the present invention. Detailed Implementation

[0042] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0043] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0044] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. These drawings are simplified schematic diagrams, which are only used to illustrate the basic structure of the present invention and therefore only show the components relevant to the present invention.

[0045] Example 1:

[0046] like Figure 1 As shown in the figure, this embodiment introduces a method for nonlinear feature extraction of sound signals, including:

[0047] S1: Acquire the non-stationary sound signal to be processed;

[0048] S2: Obtain the time spectrum of the non-stationary sound signal through short-time Fourier transform, obtain the total number of instantaneous frequencies of the non-stationary sound signal based on the time spectrum, and set the total number of instantaneous frequencies as the total number of iterations of the nonlinear feature extraction method of the sound signal; the nonlinear feature extraction method of the sound signal is the RDSSCET method, which extracts nonlinear features through recursive demodulation and noise reduction and synchronous spline kernel wavelet extraction transform;

[0049] S3: Iterative extraction of non-stationary sound signals is performed until the total number of iterations is completed, resulting in multiple high-resolution instantaneous frequency trajectories. Each iteration includes demodulation and noise reduction followed by synchronous extraction transformation, yielding a high-resolution instantaneous frequency trajectory. The synchronous spline kernel wavelet extraction transformation gathers the dispersed time-frequency energy into a time-frequency ridge and performs nonlinear feature extraction. The time-frequency ridge is the line connecting the energy peaks on the time-frequency plane that characterizes the trajectory of the instantaneous frequency of the signal as it changes over time.

[0050] S4: The time-frequency representation of multiple high-resolution instantaneous frequency trajectories is synthesized and used as the result of nonlinear feature extraction.

[0051] The non-stationary sound signal to be processed acquired in step S1 has the following expression:

[0052] (1),

[0053] In the formula, and These represent the instantaneous amplitude and instantaneous phase of the non-stationary sound signal, respectively; i represents an imaginary number; the non-stationary sound signal to be processed refers to a sound signal with nonlinear characteristics in a noisy environment;

[0054] Step S2 obtains the time spectrum of the non-stationary sound signal through short-time Fourier transform (STFT), obtains the total number of instantaneous frequencies of the non-stationary sound signal in the time spectrum, and sets the total number of instantaneous frequencies as the total number of iterations for nonlinear feature extraction of the sound signal.

[0055] Equation (1) is expressed using STFT as follows:

[0056] (2),

[0057] In the formula, Represents the window function. This represents the signal to be analyzed.

[0058] Step S2 specifically includes:

[0059] A short-time Fourier transform is performed on the non-stationary sound signal to obtain its time spectrum. The amplitude spectrum of the non-stationary sound signal is then calculated based on the time spectrum, and the fundamental frequency is extracted from the amplitude spectrum as the reference instantaneous frequency.

[0060] Based on the reference instantaneous frequency, harmonic theory assumptions, and preset frequency limits, the instantaneous frequencies of the remaining harmonics in the time spectrum are estimated. The harmonic theory assumption states that the instantaneous frequencies of each harmonic are integer multiples of the fundamental frequency. The preset frequency limits are either Nyquist frequency limits or preset frequency threshold limits. A Nyquist frequency limit means that the harmonic frequency does not exceed half the sampling frequency, while a preset frequency threshold means that the harmonic frequency does not exceed a preset frequency threshold. In this embodiment, as... Figure 3 As shown, the preset frequency limit is set to a preset threshold limit, and the preset threshold is 1500Hz;

[0061] The reference instantaneous frequency and the instantaneous frequencies of the remaining harmonics that meet the preset frequency limit are combined to obtain the total number of instantaneous frequencies of the non-stationary sound signal in the time spectrum.

[0062] The amplitude spectrum of a non-stationary sound signal is calculated based on the time-frequency spectrum. This means selecting a specific moment in the time-frequency spectrum, extracting the frequency spectrum at that moment, and obtaining the amplitude spectrum at that moment. In this embodiment, for example... Figure 3 As shown, the amplitude spectrum is selected at the 1st second to obtain 5 instantaneous frequencies of the non-stationary sound signal.

[0063] Each iteration of step S3 specifically includes:

[0064] S31: Demodulate and reduce noise for the non-stationary audio signal in the current iteration, including:

[0065] S311: Model non-stationary sound signals as a superposition of multiple non-stationary signal components and noise components;

[0066] S312: Select one non-stationary signal component from multiple non-stationary signal components and perform carrier demodulation transformation to convert it into a non-stationary signal component with time-invariant frequency.

[0067] S313: Extract the demodulated non-stationary signal component at the optimal carrier frequency that meets the bandpass filtering target by bandpass filtering;

[0068] S314: The filtered and demodulated non-stationary signal components are restored to the original non-stationary signal components through carrier reconstruction, thus obtaining the denoised non-stationary signal components of the current iteration.

[0069] The demodulation and noise reduction processing in this embodiment transforms the processing of non-stationary signal components into time-invariant domain processing through three steps: demodulation, filtering, and reconstruction. This process preserves the physical characteristics of the signal while achieving noise separation.

[0070] A demodulation and noise reduction process specifically includes:

[0071] Non-stationary sound signals are contaminated by a large number of noise components; therefore, a non-stationary sound signal can be modeled as the sum of multiple non-stationary signal components and noise components. Thus, a non-stationary sound signal... Represented as:

[0072] (3),

[0073] In the formula, It is 1 to Summation operation; It refers to the number of non-stationary signal components. In this embodiment, The value of is 5; It is the sequence number of the non-stationary mode signal component; It is the first One non-stationary signal component; It is the first The instantaneous amplitude of a non-stationary signal component; It is the first The instantaneous frequency of a non-stationary signal component; This represents the noise component.

[0074] For the The process of demodulating a non-stationary signal component is expressed as follows:

[0075] (4),

[0076] In the formula, It is the demodulation of the first One non-stationary signal component; It is a demodulation term. It is the instantaneous frequency of the demodulated signal, and It is the carrier frequency of the demodulated signal. Assuming Equation (4) can be rewritten as:

[0077] (5),

[0078] From equation (5), we can see that At carrier frequency The following is frequency-time invariant. The goal of bandpass filtering is to select the optimal carrier frequency such that the corresponding non-stationary signal component has the narrowest bandwidth and most concentrated energy after demodulation. In other words, it minimizes the bandwidth of the demodulated non-stationary signal component by optimizing the carrier frequency, thereby achieving accurate separation of the non-stationary signal component. The optimal carrier frequency refers to the center frequency that can most clearly separate a non-stationary signal component from a noisy non-stationary audio signal. In this case, when the carrier frequency... When the frequency is the same as the center frequency, that is, at the optimal carrier frequency, the non-stationary signal component of the demodulated signal is extracted to complete the bandpass filtering. The bandpass filtering extracts the first... The expression for a non-stationary signal component is:

[0079] (6),

[0080] in, It is the demodulated first part extracted by bandpass filtering. A non-stationary signal component, It is a bandpass filtering process.

[0081] Subsequently, the non-stationary signal component after filtering and demodulation in the time-invariant domain needs to be restored to the original non-stationary signal component in the time domain to obtain the denoised non-stationary signal component, expressed as:

[0082] (7),

[0083] In the formula, It is the first after noise reduction One non-stationary signal component; It is the inverse demodulation term. Used to Restored to the time-varying components in the time domain.

[0084] S32: Perform synchronous spline kernel wavelet extraction and transformation on the denoised non-stationary signal components of the current iteration to obtain a high-resolution instantaneous frequency trajectory, including:

[0085] S321: Perform time-frequency transformation on the non-stationary signal components of the current iteration to obtain the synchronous spline kernel wavelet extraction transform coefficients at each frequency at the current moment;

[0086] S322: Perform peak detection on the amplitude of the transform coefficients extracted from the synchronous spline kernel wavelet at each frequency at the current time, and take the frequency corresponding to the peak value of the amplitude as the instantaneous frequency estimate at the current time.

[0087] S323: Combine the instantaneous frequency estimates at each moment in chronological order to obtain the instantaneous frequency trajectory corresponding to the non-stationary signal component of the current iteration.

[0088] The construction process of the synchronous spline kernel wavelet extraction transform in this embodiment is as follows:

[0089] Spline-kernelled chirplet transform (SCT) is a time-frequency analysis method that constructs frequency rotation and frequency shift operators by fitting the instantaneous frequency trajectory using piecewise polynomials. It is used to match demodulate signals with nonlinear characteristics, thereby obtaining a high-resolution time-frequency representation on the time-frequency plane to accurately extract the instantaneous frequency trajectory of the signal. In this embodiment, the Synchro Spline-kernelled Chirplet Extracting Transform (SSCET) is based on the SCT, with the addition of a Synchroextracting Transform (SET) and the construction of a Spline SynchroExtracting Operator (SSEO). SET, based on the STFT, uses the synchronous extraction operator to directly extract the coefficients of the time-frequency ridge position, resulting in a time-frequency representation with highly concentrated time-frequency energy. SSCET combines the nonlinear feature extraction capability of SCT with the energy concentration characteristics of SET. SSCET directly extracts the coefficients of the time-frequency ridge position after matched demodulation of a signal with nonlinear characteristics using SSEO, that is, it gathers the dispersed time-frequency energy into the time-frequency ridge and performs nonlinear feature extraction.

[0090] The construction process of the synchronous spline kernel wavelet extraction transform includes:

[0091] The non-stationary sound signal is divided into multiple continuous spline intervals on the time axis. The spline interval at time t is: , This represents the starting time of the spline interval at time t. This represents the end time of the spline interval at time t; for the denoising... One non-stationary signal component Performing spline kernel frequency-modulated wavelet transform (SCT), the expression for the SCT at time t is:

[0092] (8),

[0093] (9),

[0094] (10)

[0095] In the formula, This represents the current time variable within the spline interval at time t; Indicates instantaneous angular frequency; This represents a frequency rotation operator constructed from spline kernels, used to match and cancel nonlinear instantaneous frequency changes in nonstationary signal components; This indicates a frequency shift operator constructed from spline kernels, used to shift the residual frequency offset in the non-stationary signal component after processing by the frequency rotation operator to a specified position, where the specified position refers to zero frequency; Represents window functions; Represents the time variable of integration. This represents the time delay of a non-stationary signal component during the transformation process. Indicates at time Frequency rotation operator; Indicates at time Frequency shift operator; Indicates at time The first noise reduction One non-stationary signal component; This represents an exponential function with the natural constant e as its base. Let represent the complex constant in the spline interval at time t; Represents the imaginary unit; This represents the summation operation over polynomials of order 1 to M; The spline coefficients represent the m-th order polynomial of the spline interval at time t. The spline kernel is a transform kernel function that uses a polynomial within a piecewise spline interval to fit the instantaneous frequency and construct a phase function for matched demodulation of non-stationary signals. The frequency rotation operator and the frequency shift operator work together to accurately match and demodulate the nonlinearly changing instantaneous frequency components in non-stationary signal components. The initial spline kernel parameters for the spline kernel frequency modulated wavelet transform (SCT) are set by first extracting the instantaneous frequency trajectory of the non-stationary sound signal through STFT, performing piecewise polynomial spline fitting on the trajectory, solving for the spline coefficients of each order polynomial corresponding to the spline interval at each time, and then recursively obtaining the complex constants within the spline interval at each time based on the continuity constraint of the spline interval.

[0096] The original synchronous extraction transform (SET) method is only effective for signals that satisfy the local stationarity assumption. If the noise reduction... If the instantaneous frequency of the nth non-stationary signal component can be considered constant within the local time covered by the window function, then the local stationarity assumption of the Synchronous Extraction Transform (SET) is satisfied. Specifically, this means that within the local time covered by the window function, if the instantaneous frequency of the nth non-stationary signal component is constant, then the local stationarity assumption of the synchronous extraction transform (SET) is satisfied. The instantaneous frequency change of the non-stationary signal component can be ignored, which is the first step in noise reduction. If the instantaneous frequency of the nth non-stationary signal component is approximately constant, then the noise reduction... A non-stationary signal component satisfies the local stationarity assumption of the Synchronous Extraction Transform (SET), and the SET can extract its time-frequency energy as a time-frequency ridge.

[0097] Similarly, in the Recursive Demodulated Synchro Spline-kernelled Chirplet Extracting Transform (RDSSCET) method of this embodiment, the Synchro Spline-kernelled Chirplet Extracting Transform (SSCET) is an addition of the Synchro Extraction Transform (SET) to the Spline Kernel Frequency Modulated Wavelet Transform (SCT), and it also needs to satisfy the local stationarity assumption. Therefore, equation (8) can be restated as follows:

[0098] (11),

[0099] In the formula, It is a newly designed window function, which is an older window function. The product of the frequency rotation and shift operators, Through the newly designed window functions The characteristic components in the time-frequency representation are the first denoising components. The instantaneous frequency of a non-stationary signal component can be considered as relative to... It remains unchanged, satisfying the local stationarity assumption of the synchronous extraction transform SET.

[0100] In a local region where the assumption of local stationarity holds, we can assume the existence of an ideal time-frequency representation whose time-frequency energy is concentrated on the instantaneous frequency trajectory. Based on this ideal time-frequency representation assumption, we can derive the expression for the instantaneous frequency trajectory.

[0101] Therefore, based on the ideal time-frequency representation assumption, equation (11) can be further expressed as:

[0102] (12),

[0103] In the formula, , This indicates the denoised time t after noise reduction. One non-stationary signal component; express The instantaneous amplitude at time t; express The instantaneous phase at time t; Represents the newly designed window function Fourier transform; The instantaneous frequency trajectory is an ideal two-dimensional instantaneous angular frequency trajectory extracted and transformed by synchronous spline kernel wavelet.

[0104] Under the assumption of time-frequency representation, the instantaneous frequency trajectory can be directly calculated by the phase change rate, according to the partial derivative of equation (12) with respect to time. To obtain the instantaneous frequency trajectory, the partial derivative at time t is as follows:

[0105] (13)

[0106] In the formula, Indicates instantaneous phase Partial derivative with respect to time, ; represents an imaginary number;

[0107] The instantaneous frequency trajectory can then be represented as:

[0108] (14)

[0109] Through formula (11). The following calculations can be performed:

[0110] (15)

[0111] In the formula, It is a newly designed window function Partial derivative with respect to time, .

[0112] Through equations (14) and (15),

[0113] according to The final instantaneous frequency trajectory is obtained. The calculation formula is:

[0114] (16)

[0115] Then, the binary fetch operator in the Dirichlet function is referenced. Used to obtain instantaneous frequency trajectory The time-frequency coefficients are expressed as follows:

[0116] (17)

[0117] In this embodiment, SSCET performs binary extraction by adding a Dirichlet function to the synchronous extraction transform SET, which forces energy to concentrate on the instantaneous frequency trajectory and eliminates energy diffusion in non-ridge regions on the time-frequency plane.

[0118] Therefore, based on equations (16) and (17), the spline kernel synchronous extraction operator based on the Dirichlet function can be obtained. The preliminary expression of the spline kernel synchronous extraction operator SSEO is:

[0119] (16)

[0120] However, considering the computational error and the need to use the real part of complex numbers in practical applications, equation (16) is rewritten as the final determined SSEO expression:

[0121] (17)

[0122] In the formula, This indicates taking the real part of a complex number; This indicates a preset discrete frequency interval. The range of values ​​is Developed through debugging based on actual application. The preset value; Equation (17) marks the complex real part less than the preset discrete frequency interval as valid and outputs the calculation result 1, and marks the complex real part not less than the preset discrete frequency interval as invalid and outputs the calculation result 0. The preset discrete frequency interval is used to limit the range of time-frequency points near the time-frequency ridge.

[0123] To improve the stability of the spline kernel synchronous extraction operator in practical applications, the real part of the complex number is extracted, and a preset discrete frequency interval is introduced to suppress noise interference outside the interval, ultimately resulting in the optimized spline kernel synchronous extraction operator SSEO. SSEO directly extracts the required instantaneous frequency without relying on traditional ridge detection.

[0124] Based on equation (17), the proposed mathematical expression for SSCET is as follows:

[0125] (17)

[0126] In the formula, This indicates the instantaneous angular frequency at time t. Synchronous spline kernel wavelet extraction of transform coefficients;

[0127] Peak detection is performed on the amplitudes of the synchronous spline kernel wavelet transform coefficients at each instantaneous angular frequency at time t to obtain the estimated instantaneous frequency at time t; the formula for calculating the instantaneous frequency at time t is:

[0128] (18)

[0129] In the formula, This represents the estimated instantaneous frequency at time t; Indicates the amplitude value; Indicates the instantaneous angular frequency at time t. The amplitude of the transform coefficients is extracted using synchronous spline kernel wavelet; This indicates the position of the maximum value of the output on the frequency axis; This indicates the position with the largest amplitude on the output frequency axis;

[0130] Synchronous Spline Kernel Wavelet Extraction Transform (SSCET) is essentially a time-frequency transform. In this embodiment, SSCET will transform the denoised nth wavelet wavelet into a time-frequency transform. The non-stationary signal component is mapped onto the time-frequency plane. For a given time t, the output of SSCET is a function of angular frequency, which represents the denoised signal component at time t. The energy and phase of each frequency component in a non-stationary signal component; for a non-stationary signal component, the energy will be concentrated near the instantaneous frequency in the time-frequency plane. Therefore, by comparing the amplitudes at all frequencies, that is, by comparing the amplitudes of the synchronous spline kernel wavelet extract transform coefficients at each instantaneous angular frequency at time t, the frequency with the largest amplitude is the estimated instantaneous frequency at time t.

[0131] S33: After completing the current iteration, update the spline kernel parameters of the frequency rotation operator and the frequency shift operator with the instantaneous frequency trajectory corresponding to the denoised non-stationary signal component of the current iteration, so that the spline kernel can more accurately match and demodulate the non-stationary signal; specifically, this means: update the obtained denoised... The instantaneous frequency trajectory corresponding to each non-stationary signal component is fitted to the frequency change in each spline interval. The spline coefficients of each order polynomial and the complex constants in the spline interval are used as new spline kernel parameters.

[0132] Step S33 further includes: after completing the current iteration round, separating the instantaneous frequency trajectory extracted in the current iteration round from the non-stationary sound signal, using the remaining part as the updated non-stationary sound signal, and performing the next iteration extraction on the updated non-stationary sound signal until the total number of iterations is completed. Specifically, this means:

[0133] The noise reduction process involves separating the non-stationary audio signal to be processed in step S1. The instantaneous frequency trajectory corresponding to each non-stationary signal component is used as the updated non-stationary sound signal. The updated non-stationary sound signal is used as the input for the next iteration. The updated non-stationary sound signal is demodulated, denoised, and extracted and transformed by synchronous spline kernel wavelet to obtain a high-resolution instantaneous frequency trajectory for the next iteration. The iteration is repeated until the total number of iterations is completed.

[0134] The total number of iterations is to separate all non-stationary signal components in the non-stationary sound signal to be processed in step S1 of equation (3), and obtain a high-resolution instantaneous frequency trajectory for each component, which can be applied to subsequent time-frequency analysis. By analyzing the changing trend of the high-resolution instantaneous frequency trajectory, the inherent nonlinear behavior characteristics in the sound signal are revealed, which can improve the accuracy of the nonlinear characteristic analysis of the sound signal.

[0135] To verify the effectiveness of the nonlinear feature extraction method for sound signals in this embodiment, a measured male voice data was used for verification. The male voice data consisted of different pitches of "a...", and the sampling frequency of the sound data was 48kHz. Two electric fans were simultaneously running next to the sound source to increase fan noise interference and simulate non-stationary sound signals. Similarly, due to the limited configuration of the computer, the speech signal also needed to be downsampled. The time waveform and Fourier spectrum of the collected male voice data are shown in Figure (2). To verify the nonlinear feature extraction effect of the nonlinear feature extraction method for sound signals in this embodiment, it was compared with the Short Time Fourier Transform (STFT). Figure (3) shows the time-frequency representation result of STFT. Figure (3)a is a schematic diagram of the overall time-frequency representation result of the short-time Fourier transform output of the collected male voice data. Figure (3)b is a local magnified view of the low-frequency region output of the short-time Fourier transform output of the collected male voice data. It can be seen that the time-varying harmonic components are submerged by noise. The instantaneous frequency trajectory can be vaguely seen, but it is difficult to identify accurately. In particular, the fundamental frequency and second harmonic components in the low-frequency region shown in Figure (3)b are more blurred than other instantaneous frequency trajectories. In contrast, as shown in Figure (4), after processing by the nonlinear feature extraction method of the sound signal in this embodiment, a high-resolution time-frequency representation result is obtained. Figure (4)a is a schematic diagram of the overall time-frequency representation result of the nonlinear feature extraction method of the sound signal in this embodiment output of the collected male voice data. Figure (4)b is a local magnified view of the low-frequency region output of the nonlinear feature extraction method of the sound signal in this embodiment output of the collected male voice data. It effectively eliminates noise interference and successfully presents five high-resolution instantaneous frequency trajectories, including the fundamental frequency and second harmonic components that are difficult to present clearly by STFT. Experimental results show that the nonlinear feature extraction method for audio signals in this embodiment performs better in terms of noise suppression and weak feature extraction, and can obtain high-resolution time-frequency representation results, thereby improving the accuracy of subsequent nonlinear feature analysis of audio signals.

[0136] Example 2

[0137] Based on the same inventive concept as Embodiment 1, this embodiment introduces a nonlinear feature extraction device for sound signals, including: a signal acquisition module, a preprocessing module, a feature extraction module, and an output module;

[0138] The signal acquisition module is used to: acquire non-stationary sound signals to be processed;

[0139] The preprocessing module is used to: obtain the time spectrum of the non-stationary sound signal through short-time Fourier transform, obtain the total number of instantaneous frequencies of the non-stationary sound signal based on the time spectrum, and set the total number of instantaneous frequencies as the total number of iterations of the nonlinear feature extraction method of the sound signal;

[0140] The feature extraction module is used to: iteratively extract non-stationary sound signals until the total number of iterations is completed, and obtain multiple high-resolution instantaneous frequency trajectories; each iteration includes: demodulating and denoising the non-stationary sound signals and performing synchronous spline kernel wavelet extraction transformation to obtain a corresponding high-resolution instantaneous frequency trajectory; the synchronous spline kernel wavelet extraction transformation gathers the dispersed time-frequency energy into time-frequency ridges and performs nonlinear feature extraction;

[0141] The output module is used to synthesize multiple high-resolution instantaneous frequency trajectories into a time-frequency representation result, which is used as the nonlinear feature extraction result corresponding to the non-stationary sound signal to be processed.

[0142] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0143] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0144] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0145] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0146] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for extracting nonlinear features of a sound signal, characterized by, include: Acquire non-stationary sound signals to be processed; The time spectrum of the non-stationary sound signal is obtained by short-time Fourier transform. The total number of instantaneous frequencies of the non-stationary sound signal is obtained based on the time spectrum, and the total number of instantaneous frequencies is set as the total number of iterations of the nonlinear feature extraction method of the sound signal. The non-stationary sound signal is iteratively extracted until the total number of iterations is completed, resulting in multiple instantaneous frequency trajectories; Each iteration of extraction includes: demodulating and denoising the non-stationary sound signal and extracting and transforming it with synchronous spline kernel wavelet to obtain a corresponding instantaneous frequency trajectory; The time-frequency representation of multiple instantaneous frequency trajectories is synthesized and used as the nonlinear feature extraction result corresponding to the non-stationary sound signal to be processed.

2. The method for nonlinear feature extraction of sound signals according to claim 1, characterized in that, The process of obtaining the time spectrum of the non-stationary sound signal through short-time Fourier transform, and obtaining the total number of instantaneous frequencies of the non-stationary sound signal based on the time spectrum, includes: A short-time Fourier transform is performed on the non-stationary sound signal to obtain its time spectrum. The amplitude spectrum of the non-stationary sound signal is then calculated based on the time spectrum, and the fundamental frequency is extracted from the amplitude spectrum as the reference instantaneous frequency. Based on the reference instantaneous frequency, harmonic theory assumptions, and preset frequency limits, estimate the instantaneous frequencies of the remaining harmonics in the time spectrum; the preset frequency limits are either Nyquist frequency limits or preset frequency threshold limits. The Nyquist frequency limit means that the frequency of the harmonic does not exceed half of the sampling frequency, and the preset frequency threshold means that the frequency of the harmonic does not exceed a preset frequency threshold. The reference instantaneous frequency and the instantaneous frequencies of the remaining harmonics that meet the preset frequency limit are combined to obtain the total number of instantaneous frequencies of the non-stationary sound signal in the time spectrum.

3. The method of nonlinear feature extraction of a sound signal according to claim 1, wherein, The demodulation and noise reduction include: The non-stationary sound signal is modeled as a superposition of multiple non-stationary signal components and noise components; Select one non-stationary signal component from multiple non-stationary signal components and perform carrier demodulation transformation to convert it into a demodulated non-stationary signal component. The non-stationary signal component is extracted at the optimal carrier frequency that meets the bandpass filtering objective by using bandpass filtering. The filtered and demodulated non-stationary signal components are restored to the original non-stationary signal components through carrier reconstruction, thus obtaining the denoised non-stationary signal components of the current iteration.

4. The method according to claim 3, wherein The non-stationary signal component undergoing noise reduction in the current iteration is subjected to synchronous spline kernel wavelet extraction transform to obtain a corresponding instantaneous frequency trajectory, including: Perform time-frequency transformation on the non-stationary signal components of the current iteration to obtain the synchronous spline kernel wavelet extraction transform coefficients at each frequency at the current moment; Peak detection is performed on the amplitude of the transform coefficients extracted from the synchronous spline kernel wavelet at each frequency at the current moment, and the frequency corresponding to the peak value of the amplitude is used as the instantaneous frequency estimate at the current moment. By combining the instantaneous frequency estimates at each moment in chronological order, the instantaneous frequency trajectory corresponding to the non-stationary signal component in the current iteration is obtained.

5. The method according to claim 4, wherein The synchronous spline kernel wavelet extraction transform is based on the spline kernel frequency-modulated wavelet transform, with the addition of synchronous extraction transform and the construction of a spline kernel synchronous extraction operator. After matching demodulation of signals with nonlinear characteristics, the synchronous spline kernel wavelet extraction transform coefficients of the time-frequency ridge position are directly extracted using the spline kernel synchronous extraction operator.

6. The method according to claim 5, wherein The time t is at the instantaneous angular frequency The synchronous spline wavelet extraction transform coefficient calculation formula is: ， In the formula, , This represents the frequency rotation operator constructed from spline kernels. This represents the frequency shift operator constructed from spline kernels. It's a newly designed window function. Represents the time variable of integration. Indicates at time The first noise reduction A non-stationary signal component, This represents an exponential function with the natural constant e as its base. Represents the imaginary unit; This indicates the spline kernel synchronous extraction operator; Window function designed by Zhongxin The calculation formula is: ， In the formula, Represents the old window function; Indicates at time Frequency rotation operator constructed from spline kernels; Indicates at time Frequency shift operator constructed from spline kernel; spline kernel frequency-modulated wavelet transform constructs frequency rotation operator and frequency shift operator by fitting instantaneous frequency trajectory with polynomial.

7. The method according to claim 6, wherein The time t is at the instantaneous angular frequency spline kernel synchronous extraction operator The calculation formula is: ， In the formula, This indicates taking the real part of a complex number; Indicates the preset discrete frequency interval; represents an imaginary number; , It is a newly designed window function Partial derivative with respect to time.

8. The method of nonlinear feature extraction of a voice signal according to claim 6, wherein, After completing the current iteration, the spline kernel parameters of the frequency rotation operator and the frequency shift operator are updated using the instantaneous frequency trajectory corresponding to the denoised non-stationary signal component of the current iteration. This includes: fitting the frequency change on each spline interval with the instantaneous frequency trajectory corresponding to the denoised non-stationary signal component of the current iteration, and using the spline coefficients of each order polynomial and the complex constants in the spline interval as new spline kernel parameters.

9. The method of nonlinear feature extraction of a voice signal according to claim 4, wherein, After completing the current iteration round, it also includes: After separating the instantaneous frequency trajectory extracted in the current iteration from the non-stationary sound signal, the remaining part is used as the updated non-stationary sound signal. The updated non-stationary sound signal is then used for the next iteration extraction until the total number of iterations is completed.

10. An apparatus for extracting a nonlinear feature of a sound signal, characterized by comprising: include: Signal acquisition module, preprocessing module, feature extraction module, and output module; The signal acquisition module is used to: acquire non-stationary sound signals to be processed; The preprocessing module is used to: obtain the time spectrum of the non-stationary sound signal through short-time Fourier transform, obtain the total number of instantaneous frequencies of the non-stationary sound signal based on the time spectrum, and set the total number of instantaneous frequencies as the total number of iterations of the nonlinear feature extraction method of the sound signal; The feature extraction module is used to: iteratively extract non-stationary sound signals until the total number of iterations is completed, and obtain multiple instantaneous frequency trajectories; each iteration of extraction includes: demodulating and denoising the non-stationary sound signals in sequence and performing synchronous spline kernel wavelet extraction and transformation to obtain a corresponding instantaneous frequency trajectory; The output module is used to synthesize a time-frequency representation of multiple instantaneous frequency trajectories as the nonlinear feature extraction result corresponding to the non-stationary sound signal to be processed.

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