1, Get code method
Get code method 1:
The complete code has been uploaded to my resources: [digital signal processing] synchronous compression and transformation of digital signals based on MATLAB [including Matlab source code 1534]
Get code method 2:
By subscribing to the payment column of zijishenguang blog, private bloggers can obtain this code with payment vouchers.
Note: if you subscribe to the paid column of zijishenguang blog, you can get a code for free (valid for three days from the Subscription Date);
2, Introduction to synchronous compression transformation
Based on WT, SST uses synchronous compression operator to improve the resolution of time-frequency ridge in time spectrum, and realizes the extraction and reconstruction of instantaneous frequency. set up ψ (b) Is the wavelet generating function, then the continuous wavelet transform of signal x(t) is:
Where:
x(t) - vibration signal;
W(a,b) - continuous wavelet transform result of x(t);
t -- time variable;
a - scale factor;
b -- translation factor;
According to the analysis, the instantaneous frequency information of position (a,b) in the wavelet domain is:
Where:
ω x(a,b) - instantaneous frequency;
j -- imaginary unit.
Literature [10] found that no matter what value a is, the oscillation characteristics of W(a,b) on B point to the initial frequency Ω. Therefore:
According to the defined synchronous compression transform, the inverse wavelet transform is:
Where:
x(b) - result of inverse wavelet transform;
C ψ—— Phase difference coefficient;
ψ (a ξ)—— Wavelet generating function.
yes ω x(a,b) is integrated along the direction of scale a and classified into frequency domain ω=ω At the position of x(a,b), the synchronous compression transformation is defined as:
Where:
Sst ( ω, b) - synchronous compression function of signal B;
ω—— Angular frequency.
The result of equation (6) and phase difference coefficient C ψ, The amplitude of the signal is reduced to the position in the frequency domain, and finally the high-resolution time spectrum is obtained.
3, Partial source code
% A numerical signal. clear; SampFreq = 100; t = 0 : 1/SampFreq : 14-1/SampFreq; Sig = [sin(2*pi*(25*t))]; [m,n]=size(Sig); time=(1:n)/SampFreq; fre=(SampFreq/2)/(n/2):(SampFreq/2)/(n/2):(SampFreq/2); Ts = SST(Sig',100); figure imagesc(time,fre,abs(Ts)); axis xy ylabel('Freq / Hz'); xlabel('Time / Sec'); title('SST'); %signal reconstruction. s=real(sum(Ts)); %Reconstructed signal. figure plot(s); title('Reconstructed signal'); %Original signal figure plot(Sig,'r-'); title('Original signal'); function [Ts] = SST(x,hlength); % Computes the SST (Ts) of the signal x. % INPUT % x : Signal needed to be column vector. % hlength: The hlength of window function. % OUTPUT % Ts : The SST [xrow,xcol] = size(x); if (xcol~=1), error('X must be column vector'); end; if (nargin < 1), error('At least 1 parameter is required'); end; if (nargin < 2), hlength=round(xrow/5); end; Siglength=xrow; hlength=hlength+1-rem(hlength,2); ht = linspace(-0.5,0.5,hlength);ht=ht'; % Gaussian window h = exp(-pi/0.32^2*ht.^2); % derivative of window dh = -2*pi/0.32^2*ht .* h; % g' [hrow,hcol]=size(h); Lh=(hrow-1)/2; N=xrow; t=1:xrow; [trow,tcol] = size(t); tfr1= zeros (N,tcol) ; tfr2= zeros (N,tcol) ; tfr= zeros (round(N/2),tcol) ; Ts= zeros (round(N/2),tcol) ;
4, Operation results
5, matlab version and references
1 matlab version
2014a
2 references
[1] Shen Zaiyang. Proficient in MATLAB signal processing [M]. Tsinghua University Press, 2015
[2] Gao Baojian, Peng Jinye, Wang Lin, pan Jianshou. Signal and system -- Analysis and implementation using MATLAB [M]. Tsinghua University Press, 2020
[3] Wang Wenguang, Wei Shaoming, Ren Xin. MATLAB implementation of signal processing and system analysis [M]. Electronic Industry Press, 2018
[4] Gao Yanyan, Zhang Jing, Li Li, Jia Yingxi. Design of teaching demonstration system of digital signal processing based on GUI [J]. Education and Teaching Forum. 2019, (48)
[5] Li Jun, Zhang Shuling, Shuai Jing. Digital signal processing aided teaching system based on Matlab GUI interface [J]. Information communication. 2020, (08)
[6] Li Yijia, Wang Jing, Wang Zhengfang, Sui Qingmei. Study on denoising method of microseismic signal based on multiple synchronous compression transform [J]. Journal of applied basic and engineering sciences