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High-precision high-order time rearrangement synchronous extrusion transformation time-frequency analysis method

A technology of synchronous extrusion and time-frequency analysis, which is applied in the field of signal processing, can solve problems affecting signal processing effects and limited GD estimation accuracy, and achieve the effects of improving time-frequency readability, suppressing energy divergence, and good consistency

Active Publication Date: 2020-06-16
CHENGDU UNIVERSITY OF TECHNOLOGY
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  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, this method has limited accuracy for GD estimation, which will affect the final signal processing effect

Method used

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  • High-precision high-order time rearrangement synchronous extrusion transformation time-frequency analysis method
  • High-precision high-order time rearrangement synchronous extrusion transformation time-frequency analysis method
  • High-precision high-order time rearrangement synchronous extrusion transformation time-frequency analysis method

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Experimental program
Comparison scheme
Effect test

Embodiment 1

[0049] Example 1: see figure 1 , a high-precision high-order time rearrangement synchronous squeeze transform time-frequency analysis method, comprising the following steps:

[0050] (1) Obtain a time-domain signal x(t), perform Fourier transform to obtain a frequency-domain signal X(ω), t is time, and ω is frequency;

[0051] (2) Select order N and frequency window function G(ω), calculate X(ω) at ω k Short-time Fourier transform under G(ω) to obtain different time-frequency values ​​corresponding to time-frequency points (t,ω) Where N is a positive integer, k=0,1,2,...,max{1,2N-2}, and when k=0, G(ω)=ω 0 G(ω), use Construct N order square matrix α N (t,ω) and β N (t,ω);

[0052]

[0053]

[0054] In the formula, s is the adjustment factor in the window function G(ω);

[0055] (3) Using the N-order square matrix α N (t,ω) and β N (t,ω) to calculate the Nth order group delay estimate

[0056] When β N When the determinant value of (t,ω) is not zero, th...

Embodiment 2

[0060] Embodiment 2: It also includes step (6), obtaining the reconstructed signal x'(t) through N-order time rearrangement and synchronous squeezing inverse transformation. All the other are identical with embodiment 1.

Embodiment 3

[0061] Embodiment 3: This embodiment is the same as Embodiment 2, the difference is that in step (2), Obtained by the following formula;

[0062]

[0063]

[0064] In the formula, v is a frequency variable and is independent of the value of ω, i is the imaginary number unit, G * (ω) represents taking the complex conjugate of G(ω).

[0065] In step (3), the N-order group delay estimation is specifically calculated using the following formula

[0066]

[0067] In the formula, Im means to take the imaginary part of the complex number.

[0068] In step (4), specifically use the following formula to obtain the N-order time rearrangement synchronous extrusion transformation

[0069]

[0070] In the formula, u is a time variable, and it is a different time variable that has nothing to do with the value of t, and the function σ(x) is a Dirac function.

[0071] In step (6), specifically adopt the following formula to obtain the reconstructed signal x'(t);

[0072]...

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Abstract

The invention discloses a high-precision high-order time rearrangement synchronous extrusion transformation time-frequency analysis method. The method comprises the steps: converting a signal x (t) into a frequency domain signal X (omega); selecting an order number N and a frequency window function G (omega), calculating short-time Fourier transform of the X (omega) under omega<k>G (omega), constructing square matrixes alpha N (t, omega) and beta N (t, omega), and calculating N-order group delay estimation; superposing a time-frequency value to a GD estimation position along a time direction,and calculating N-order time rearrangement synchronous extrusion transform to obtain a time-frequency spectrum; and reconstructing the signal. According to the invention, a novel GD estimation methodis provided, the estimation precision of the rapidly changing GD is improved; and the time-frequency spectrum energy is rearranged in the time direction to be gathered near the real GD, so that the energy diffusion is effectively inhibited, and the time-frequency readability is improved. The invention further provides a reconstruction method, and the reconstruction signal is high in reduction degree.

Description

technical field [0001] The invention relates to a signal processing method, in particular to a high-precision high-order time rearrangement synchronous extrusion transformation time-frequency analysis method. Background technique [0002] Time-frequency analysis has always been an important research method for modern non-stationary signal analysis and processing. Currently commonly used time-frequency analysis methods mainly include short-time Fourier transform (STFT), continuous wavelet transform (CWT), S-transform (ST), etc. These methods based on window functions have certain defects, and are affected by the window function itself. The time-frequency resolution is limited, and the energy aggregation of the time-frequency spectrum is limited, so it is difficult to accurately extract the characteristics of the signal. [0003] In order to improve the effect of time-frequency analysis, Kodera et al. proposed a time-frequency rearrangement method, which improves the time-fre...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G01R23/02G06F17/16
CPCG01R23/02G06F17/16
Inventor 陈辉胡英杨超陈旭平冯俊魏友华郭科
Owner CHENGDU UNIVERSITY OF TECHNOLOGY
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