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Time-Frequency Analysis Method for High-Precision High-order Time-Rearrangement Synchronous Squeeze Transform

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

Active Publication Date: 2021-10-08
CHENGDU UNIVERSITY OF TECHNOLOGY
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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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  • Time-Frequency Analysis Method for High-Precision High-order Time-Rearrangement Synchronous Squeeze Transform
  • Time-Frequency Analysis Method for High-Precision High-order Time-Rearrangement Synchronous Squeeze Transform
  • Time-Frequency Analysis Method for High-Precision High-order Time-Rearrangement Synchronous Squeeze Transform

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Embodiment 1

[0049] Embodiment 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,...

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 squeeze transformation time-frequency analysis method, which includes: transforming a signal x(t) into a frequency domain signal X(ω); selecting the order N and the frequency window function G( ω), calculate X(ω) at ω k Short-time Fourier transform under G(ω), construct square matrix α N (t,ω) and β N (t, ω), calculate the N-order group delay estimation, superimpose the time-frequency value to the GD estimation along the time direction, calculate the N-order time rearrangement synchronous squeeze transformation to obtain the time spectrum; and reconstruct the signal. The present invention provides a new GD estimation method, which improves the estimation accuracy of the fast-changing GD. By rearranging the time-spectrum energy in the time direction, it gathers it near the real GD, thereby effectively suppressing the Energy divergence improves time-frequency readability. Furthermore, a reconstruction method is provided, and the restoration degree of the reconstruction signal is high.

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 Patents(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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