Short-time fractional Fourier transform time-frequency analysis method based on window decoupling

Abstract

The invention discloses a window-based decoupling short-time fractional Fourier transform time-frequency analysis method. The method comprises the following steps: S1, acquiring non-stationary signal data generated under power quality disturbance in a power grid; s2, segmenting the non-stationary signal into a plurality of parts based on signal waveform characteristics, and setting an initialized virtual window function for discrete short-time fractional Fourier transform, wherein the window function only provides an interface for calling of a specific window function; s3, calling different window functions for each segmented sub-segment signal to obtain windowed sub-segment signals under a specific window function; and S4, discrete fractional Fourier transform is applied to the sub-segment signals obtained in the step S3 to obtain time-frequency results of the sub-segment signals under different windows, and finally, frequency spectrums of the sub-segment signals are spliced according to a time sequence and output by an oscilloscope. Based on the characteristics of non-stationary signals generated under power quality disturbance in a power grid, different window function analysis signals can be called in one task by setting a virtual window function interface, and the window-based decoupling short-time fractional order Fourier transform time-frequency analysis method is formed. According to the method, the coupling between fractional Fourier transform and a specific window is reduced, the expandability of a program is improved, and more accurate signal local spectrum features can be obtained.

Description

Technical Field

[0001] The present invention relates to the field of non-stationary signal analysis generated under power quality disturbance in a power grid, and in particular to a short-time fractional-order Fourier transform time-frequency analysis method based on window decoupling. Background Art

[0002] Non-stationary signals generated by power quality disturbances in power grids are primarily characterized by transient voltage changes, swells, sags, and transient pulses. These non-stationary signal characteristics vary across different time domains. While the classic fractional-order Fourier transform (FFT) offers greater degrees of freedom than the Fourier transform (FFT), its mathematical properties prevent it from reflecting time-dependent frequency variations. In recent years, the short-time fractional-order Fourier transform (SFT), a novel non-stationary signal analysis tool that overcomes the shortcomings of the FFT, has been increasingly applied to non-stationary signal analysis in power grids.

[0003] However, applying short-time fractional-order Fourier transforms to analyze non-stationary signals generated by power quality disturbances in power grids has two major drawbacks. First, a global window function setting is currently used for a given analysis task. That is, once a window function is selected, it remains unchanged until the task is completed. This results in some windows not being able to effectively reflect local changes in the signal's morphology. For example, a rectangular window is more appropriate for signals exhibiting transient pulse characteristics, while a Hanning window is more suitable for smoother portions. Therefore, flexible window function switching based on signal characteristics is necessary. Second, changing the window requires retesting the source program, resulting in poor scalability. This invention proposes a virtual window method. This window only provides a program call interface for a specific window function, eliminating the need to set a specific window function during initialization. When analyzing a specific signal, the program interface calls the specific window function to window the signal, and then applies the discrete fractional-order Fourier transform to analyze the signal. Because the virtual window function is always accessed through the main program, calling a different window function eliminates the need to retest the source program when analyzing different signal segments. This allows for analyzing the spectral characteristics of signals with different morphologies, improves the scalability of the analysis system, and reduces testing time and costs.

[0004] Therefore, there is an urgent need for a time-frequency analysis method that can effectively and accurately analyze the local frequency characteristics of non-stationary signals generated by power quality disturbances. Summary of the Invention

[0005] In view of this, the technical problem to be solved by the present invention is to overcome the shortcomings of the fractional-order Fourier transform under the global window function while avoiding the need to recompile and test the entire source program after changing the window function in the task, which reduces its scalability and increases time costs. The present invention proposes a method for segmenting the original signal according to its characteristics and introducing a virtual window, providing an interface for calling a specific window function. This eliminates the need for recompiling and testing the main program when switching window functions, further overcoming the shortcomings of the traditional global window function and more accurately reflecting the signal video characteristics. Therefore, a time-frequency analysis method based on short-time fractional-order Fourier transform with window decoupling is invented.

[0006] The object of the present invention is achieved like this:

[0007] The present invention provides a time-frequency analysis method based on short-time fractional Fourier transform with window decoupling, comprising the following steps:

[0008] S1: Acquire non-stationary signal data generated by power quality disturbance in the power grid;

[0009] S2: Divide the non-stationary signal into several parts based on the signal waveform characteristics and set an initialized virtual window for discrete fractional Fourier transform. This window only provides a program calling interface for a specific window function.

[0010] S3: Select different window functions for each segmented signal to obtain sub-segment signal fragments of multiple time windows under the window function;

[0011] S4: Apply discrete fractional Fourier transform to each sub-segment signal obtained in step S3 to obtain the time-frequency results of each sub-segment signal under different windows, then splice the spectrum of each sub-segment signal in time sequence, and finally output it by oscilloscope.

[0012] In the step S2, the non-stationary signal is divided into several parts based on the signal waveform characteristics and an initial virtual window is set for discrete fractional Fourier transform. The window only provides a program calling interface for a specific window function. The specific steps are as follows:

[0013] S21: Based on the non-stationary signal generated by the power quality interference in the power grid, the signal is divided into several sub-signal segments according to the time domain characteristics based on the signal waveform characteristics, assuming that they are X1, X2,…,X n ;

[0014] S22: Setting a virtual window function without any functional implementation. It only needs to provide a program interface that can call commonly used different types of window functions;

[0015] In step S4, discrete fractional Fourier transform is applied to each sub-segment signal obtained in step S3 to obtain the time-frequency results of each sub-segment signal under different windows. Then, the spectrum of each sub-segment signal is spliced in time sequence and finally output by the oscilloscope. The specific steps are as follows:

[0016] S41: According to steps S22 and S3, a specific window function is selected for the X1 signal segment according to the characteristics of the source signal, and the windowed signal is obtained and discretized;

[0017] S42: Initialize the parameters of discrete fractional Fourier transform. The general expression is The kernel function x w [n] is the discretized windowed signal, p is the order of the fractional order, and The angle of rotation of the time-frequency plane can be controlled, N is the signal length, k is the index of the fractional-order domain, corresponding to the discretized fractional-order frequency;

[0018] S43: Repeat steps S41 and S42 to analyze the spectrum of the remaining signal segments. In this process, different window functions can be selected for different signal segments to avoid global fixed window function analysis;

[0019] S44: After the analysis is completed through the above steps, the signal spectra of each sub-segment are spliced in time sequence and finally output by the oscilloscope.

[0020] The advantages of the present invention are that it proposes a method for segmenting the original signal based on characteristics and introducing a virtual window, providing an interface for calling specific window functions. This eliminates the need for recompiling and testing the main program when switching window functions, and further overcomes the shortcomings of traditional global window functions. Due to the ability to flexibly switch window functions, compared to traditional global window function analysis, the invention provides better analysis results for non-stationary signals with variable characteristics. For example, if transient mutations or pulse-like signal characteristics appear in the signal, the virtual window can be switched to a rectangular window. If frequency modulation-like signal characteristics appear, a Gaussian window can be switched, thereby more accurately reflecting the signal's spectral characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0022] Figure 1 This is a flow chart of a time-frequency analysis method based on short-time fractional Fourier transform with window decoupling;

[0023] Figure 2 Flowchart for window decoupling analysis.

[0024] Specific implementation details

[0025] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the preferred embodiments are only for illustrating the present invention, rather than for limiting the scope of protection of the present invention.

[0026] Figure 1 This is a flow chart of a time-frequency analysis method based on short-time fractional Fourier transform with window decoupling. Figure 2 The flowchart of the window decoupling analysis is shown in the figure: The present invention provides a short-time fractional Fourier transform time-frequency analysis method based on window decoupling, which includes the following steps:

[0027] S1: Acquire non-stationary signal data generated by power quality disturbance in the power grid;

[0028] S2: Divide the non-stationary signal into several parts based on the signal waveform characteristics and set an initialized virtual window for discrete fractional Fourier transform. This window only provides a program calling interface for a specific window function.

[0029] S3: Select different window functions for each segmented signal to obtain sub-segment signal fragments of multiple time windows under the window function;

[0030] S4: Apply discrete fractional Fourier transform to each sub-segment signal obtained in step S3 to obtain the time-frequency results of each sub-segment signal under different windows, then splice the spectrum of each sub-segment signal in time sequence, and finally output it by oscilloscope.

[0031] In the step S2, the non-stationary signal is divided into several parts based on the signal waveform characteristics and an initial virtual window is set for discrete fractional Fourier transform. The window only provides a program calling interface for a specific window function. The specific steps are as follows:

[0032] S21: Based on the non-stationary signal generated by the power quality interference in the power grid, the signal is divided into several sub-signal segments according to the time domain characteristics based on the signal waveform characteristics, assuming that they are X1, X2,…,X n ;

[0033] S22: Setting a virtual window function without any functional implementation. It only needs to provide a program interface that can call commonly used different types of window functions;

[0034] In step S4, discrete fractional Fourier transform is applied to each sub-segment signal obtained in step S3 to obtain the time-frequency results of each sub-segment signal under different windows. Then, the spectrum of each sub-segment signal is spliced in time sequence and finally output by the oscilloscope. The specific steps are as follows:

[0035] S41: According to steps S22 and S3, a specific window function is selected for the X1 signal segment according to the characteristics of the source signal. For example, a rectangular window is applied to the transient mutation signal. The general expression is Where L is the rectangular window length, which is generally smaller than the signal length. When encountering a signal segment with FM characteristics, the Gaussian window can be switched. The general expression is Where μ is the center position of the window, σ is the width of the control window, and the windowed signal is obtained and discretized;

[0036] S42: Initialize the parameters of discrete fractional Fourier transform. The general expression is The kernel function x w [n] is the discretized windowed signal, p is the order of the fractional order, and The angle of rotation of the time-frequency plane can be controlled, N is the signal length, k is the index of the fractional-order domain, corresponding to the discretized fractional-order frequency;

[0037] S43: Repeat steps S41 and S42 to analyze the spectrum of the remaining signal segments. In this process, different window functions can be selected for different signal segments to avoid global fixed window function analysis;

[0038] S44: After the analysis is completed through the above steps, the signal spectra of each sub-segment are spliced in time sequence and finally output by the oscilloscope.

[0039] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. It is apparent that various modifications and variations may be made by those skilled in the art without departing from the spirit and scope of the present invention. Thus, the present invention is intended to encompass such modifications and variations as long as they fall within the scope of the claims and their equivalents.

Claims

1. A time-frequency analysis method based on short-time fractional Fourier transform with window decoupling, characterized by: The following steps are involved: S1: Acquire non-stationary signal data generated by power quality disturbance in the power grid; S2: Divide the non-stationary signal into several parts based on the signal waveform characteristics and set an initialized virtual window for discrete short-time fractional Fourier transform. This window only provides a program calling interface for a specific window function. S3: Select different window functions for each segmented signal to obtain sub-segment signal fragments of multiple time windows under the window function; S4: Apply discrete fractional Fourier transform to each sub-segment signal obtained in step S3 to obtain the time-frequency results of each sub-segment signal under different windows, then splice the spectrum of each sub-segment signal in time sequence, and finally output it by oscilloscope. In the step S2, the non-stationary signal is divided into several parts based on the signal waveform characteristics and an initial virtual window is set for discrete fractional Fourier transform. The window only provides a program calling interface for a specific window function. The specific steps are as follows: S21: Based on the non-stationary signal generated by the power quality interference in the power grid, the signal is divided into several sub-signal segments according to the signal waveform characteristics, assuming that they are X1, X2,…, X n ; S22: Setting a virtual window function without any functional implementation. It only needs to provide a program interface that can call commonly used different types of window functions; In step S4, discrete fractional Fourier transform is applied to each sub-segment signal obtained in step S3 to obtain the time-frequency results of each sub-segment signal under different windows. Then, the spectrum of each sub-segment signal is spliced in time sequence and finally output by the oscilloscope. The specific steps are as follows: S41: According to steps S22 and S3, a specific window function is selected for the X1 signal segment according to the characteristics of the source signal, and the windowed signal is obtained and discretized; S42: Initialize the parameters of discrete fractional Fourier transform. The general expression is The kernel function x w [n] is the discretized windowed signal, p is the order of the fractional order, and The angle of rotation of the time-frequency plane can be controlled, N is the signal length, k is the fractional-order domain index, corresponding to the discretized fractional-order frequency; S43: Repeat steps S41 and S42 to perform spectrum analysis on the remaining signal segments in sequence. In this process, different window functions can be called for different signal segments to avoid global fixed window function analysis. S44: After the analysis is completed through the above steps, the signal spectra of each sub-segment are spliced in time sequence and finally output by the oscilloscope.

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