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Fractional order synchronous extraction generalized S transformation time-frequency decomposition and reconstruction method

A technology of synchronous extraction and time-frequency decomposition, which is applied in the direction of complex mathematical operations to achieve the effect of time-frequency energy concentration and time-frequency resolution improvement

Active Publication Date: 2019-10-18
CHENGDU UNIVERSITY OF TECHNOLOGY
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  • Application Information

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Problems solved by technology

However, this method is essentially a time-frequency analysis post-processing technology, so it has a certain dependence on the time-frequency resolution of the original time-frequency method.

Method used

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  • Fractional order synchronous extraction generalized S transformation time-frequency decomposition and reconstruction method
  • Fractional order synchronous extraction generalized S transformation time-frequency decomposition and reconstruction method
  • Fractional order synchronous extraction generalized S transformation time-frequency decomposition and reconstruction method

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Embodiment 1

[0052] Embodiment 1: see figure 1 , a fractional-order synchronous extraction generalized S-transform time-frequency decomposition and reconstruction method, comprising the following steps:

[0053] (1) Input the original one-dimensional signal x(t) to be analyzed;

[0054] (2) Perform fractional Fourier transform spectrum analysis on the one-dimensional signal x(t) with different rotation angles α, and determine the concentration degree of signal energy according to the size of the spectral coefficients, and select the corresponding time when the signal energy concentration is the strongest The rotation angle of , which is regarded as the optimal rotation angle αo pt ;

[0055] Described step (2) is specifically:

[0056] Select the optimal rotation angle α according to the following formula opt

[0057]

[0058] In the formula, t is time, u is fractional frequency, K α (t,u) is the transform kernel of fractional Fourier transform, and its expression is:

[0059] ...

Embodiment 2

[0080] (1) Input the original one-dimensional signal x(t) to be analyzed. In this embodiment, the one-dimensional signal x(t) is figure 2 Shown is the composite signal sig of two linear signals sig1 and sig2.

[0081] Steps (2)-(7) are the same as in Example 1.

[0082] The present embodiment also includes between steps (6) and (7), and also includes a step of: performing a modulo operation on the result in step (6) to obtain the final fractional order synchronously extracting the generalized S-transform time spectrum At this time, the time-spectrum diagram after this step is processed is as follows image 3 . from image 3 It can be seen that after being processed by the method of the present invention, the time spectrum of the two linear sub-signals can be correctly presented, the frequency increases linearly with time, the frequency resolution is high, and the energy is concentrated.

Embodiment 3

[0084] (1) Input the original one-dimensional signal x(t) to be analyzed. In this embodiment, the one-dimensional signal x(t) is Figure 4 Shown is the composite signal sig of two nonlinear signals sig1 and sig2.

[0085] Steps (2)-(7) are the same as in Example 1.

[0086] The present embodiment also includes between steps (6) and (7), and also includes a step of: performing a modulo operation on the result in step (6) to obtain the final fractional order synchronously extracting the generalized S-transform time spectrum At this time, the time-spectrum diagram after this step is processed is as follows Figure 5 . from Figure 5 It can be seen that the processed time-spectrum has two curves, corresponding to the time-spectrum of two nonlinear signals, the frequency changes in a curve with time, the frequency resolution is high, and the energy is concentrated.

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Abstract

The invention discloses a fractional order synchronous extraction generalized S transform time-frequency decomposition and reconstruction method. The method comprises the following steps: inputting x(t), selecting different rotation angles alpha to carry out fractional Fourier transform spectral analysis on x (t); selecting an optimal rotation angle alpha opt to carry out fractional order generalized S transformation on the signal to obtain a fractional order generalized S transform value, and performing modeling; solving fractional order instantaneous frequency estimation on the basis of thefractional order generalized S transform value, obtaining a synchronous extraction operator according to the instantaneous frequency estimation, extracting a fractional order generalized S transformtime-frequency spectrum by using the synchronous extraction operator, retaining effective energy, and finally reconstructing a signal. According to the invention, the time-frequency characterization of the signal can be popularized to the time fractional order frequency characterization; time-frequency information details can be recognized by selecting the optimal rotation angle in a self-adaptivemode, on the basis, energy of a fractional order synchronous extraction generalized S transformation time-frequency spectrum is more gathered by adjusting window function parameters and conducting extraction operation, and therefore the time-frequency resolution of signals is greatly improved.

Description

technical field [0001] The invention relates to a signal decomposition and reconstruction method, in particular to a fractional-order synchronous extraction generalized S-transform time-frequency decomposition and reconstruction method. Background technique [0002] As an important branch of non-stationary signal processing, time-frequency analysis has always been one of the research hotspots in modern signal processing. Common time-frequency analysis methods include short-time Fourier transform (STFT), wavelet transform (CWT), S-transform (ST) and generalized S-transform (GST). Among them, the "size" and "shape" of the STFT window function are fixed. In practical applications, after the window function is selected, it is difficult to ensure that the obtained results have a high enough resolution in both the time domain and the frequency domain; CWT passes The time-scale analysis of the signal can achieve the characteristics of multi-resolution, but it is essentially a Four...

Claims

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Application Information

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IPC IPC(8): G06F17/14
CPCG06F17/14
Inventor 胡英陈旭平孙绍通陈辉王元君冯俊钱红艳朱冰雪杨超陈扬
Owner CHENGDU UNIVERSITY OF TECHNOLOGY
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