High-order synchronous extraction transform signal time-frequency analysis method
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
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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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