High-order synchronous extraction transform signal time-frequency analysis method
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A technology for synchronously extracting and transforming signals, which is applied in the field of signal processing and can solve problems such as low time-frequency accuracy
Inactive Publication Date: 2019-01-01
CHENGDU UNIVERSITY OF TECHNOLOGY
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[0004] Synchronous extraction transform is essentially a time-frequency analysis post-processing technology, which is ...
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Embodiment 1
[0106] Embodiment 1: see figure 1 , a time-frequency analysis method for high-order synchronous extraction and transformation signals, comprising the following steps:
[0107] (1) Obtain Gaussian FM signal f(τ)=A(τ)·e i·2π·φ(τ) , and perform high-order Taylor series expansion on the Gaussian FM signal to obtain f N (τ), wherein, A (τ) is the amplitude, φ (τ) is the phase, τ is the time, i is the imaginary number unit, N is the order of the high-order Taylor series expansion, N≥2, and is an integer;
[0108] (2) to f N (τ) performs short-time Fourier transform to obtain the short-time Fourier transform value V e g (t, ω), where ω is the frequency modulation factor, g is the window function, and t is the time translation factor;
[0109] (3) According to V e g (t,ω), find the signal f 1 (τ) local instantaneous frequency ω(t,ω);
[0110] (4) And according to the local instantaneous frequency ω(t,ω), find the high-order instantaneous frequency of the signal Further obta...
Embodiment 2
[0137] Example 2: see Figure 2-Figure 7 , the theoretical signal is a recognized model for testing the time-frequency focusing performance of the time-frequency distribution, figure 2 The developed formula is the theoretical signal used in the implementation of Case 2, so next we will figure 2 The developed theoretical signal is used as the original signal f(τ) in step (1), and the specific implementation is the same as that in Example 1. In the present invention, the second-order synchronous extraction transformation value and the third-order synchronous extraction transformation value are respectively obtained through calculation, and the time spectrums of the second-order synchronous extraction transformation and the third-order synchronous extraction transformation are respectively obtained.
[0138] image 3 is the time spectrum of the short-time Fourier transform of the theoretical signal, Figure 4 , Figure 5 , Image 6 They are the time-spectrum of the theoret...
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Abstract
A method for analyze time-frequency of high-order synchronous extracted transform signal includes such steps as expanding high-order Taylor series, carrying out short-time Fourier transform, obtaininglocal instantaneous frequency, obtaining high-order instantaneous frequency, and obtaining high-order synchronous extracted operator, carrying out high-order Taylor series expansion, carrying out short-time Fourier transform, and obtaining high-order synchronous extracted operator. Finally, taking the frequency set after the short-time Fourier transform as the center frequency set, combined withthe high-order synchronous extraction operator, it 'extracts' the value of each time-frequency point corresponding to the instantaneous frequency in the vicinity of each center frequency, that is, only the energy near the time-frequency ridge in the time-frequency plane is reserved, and all the other divergent energy is eliminated to obtain the high-order synchronous extraction transform value. High-order synchronous extraction transform not only inherits the advantages of high time-frequency focusing and good noise robustness of synchronous extraction transform, but also has higher time-frequency precision than short-time Fourier transform and synchronous extraction transform, so it is a new time-frequency analysis method with high precision.
Description
technical field [0001] The invention relates to a signal processing method, in particular to a high-order synchronous extraction and transformation signal time-frequency analysis method. Background technique [0002] As a powerful tool for analyzing time-varying non-stationary signals, time-frequency analysis has become a hot spot in modern signal processing research. The time-frequency analysis method provides the joint distribution information of time domain and frequency domain, and clearly describes the relationship of signal frequency with time. 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 window function after the short-time Fourier transform are fixed, so the time-frequency resolution of the obtained time spectrum is the same everywhere; the wavelet base of the wavelet transform is stretching and shifting with t...
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