## [bd30d0]: / demos / demo_gabmulappr.m  Maximize  Restore  History

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94``` ```%DEMO_GABMULAPPR Approximate a slowly time variant system by a Gabor multiplier % % This script construct a slowly time variant system and performs the % best approximation by a Gabor multiplier with specified parameters % (a and L see below). Then it shows the action of the slowly time % variant system (A) as well as of the best approximation of (A) by a % Gabor multiplier (B) on a sinusoids and an exponential sweep. % % .. figure:: % % Spectrogram of signals % % The figure shows the spectogram of the output of the two systems applied on a % sinusoid (left) and an exponential sweep. % % See also: gabmulappr % AUTHOR : Peter Balazs. % based on demo_gabmulappr.m disp('Type "help demo_gabmulappr" to see a description of how this demo works.'); % Setup parameters for the Gabor system and length of the signal L=576; % Length of the signal a=32; % Time shift M=72; % Number of modulations fs=44100; % assumed sampling rate SNRtv=63; % signal to noise ratio of change rate of time-variant system % construction of slowly time variant system % take an initial vector and multiply by random vector close to one A = []; c1=(1:L/2); c2=(L/2:-1:1); c=[c1 c2].^(-1); % weight of decay x^(-1) A(1,:)=(rand(1,L)-0.5).*c; % convolution kernel Nlvl = exp(-SNRtv/10); Slvl = 1-Nlvl; for ii=2:L; A(ii,:)=(Slvl*circshift(A(ii-1,:),[0 1]))+(Nlvl*(rand(1,L)-0.5)); end; A = A/norm(A)*0.99; % normalize matrix % perform best approximation by gabor multiplier sym=gabmulappr(A,a,M); % creation of 3 different input signals (sinusoids) x=2*pi*(0:L-1)/L.'; f1 = 1000; % frequency in Hz s1=0.99*sin((fs/f1).*x); % Ramp the signal to avoid distortions at the end, ramp are 5% of total % length of the signal. s1=rampsignal(s1,round(L*.05)); L1=ceil(L*0.9); e1=0.99*expchirp(L1,500,fs/2*0.9,'fs',fs); % Ramp signal as before. e1=rampsignal(e1,round(L1*.05)); e1=[e1;zeros(L-L1,1)]; % application of the slowly time variant system As1=A*s1'; Ae1=A*e1; % application of the Gabor multiplier Gs1=gabmul(s1,sym,a); Ge1=gabmul(e1,sym,a); % Plotting the results %% ------------- figure 1 ------------------------------------------ clim=[-40,13]; figure(1); subplot(2,2,1); sgram(real(As1),'tfr',10,'clim',clim,'nocolorbar'); title (sprintf('Spectogram of output signal: \n Time-variant system applied on sinusoid'),'Fontsize',14); set(get(gca,'XLabel'),'Fontsize',14); set(get(gca,'YLabel'),'Fontsize',14); subplot(2,2,2); sgram(real(Ae1),'tfr',10,'clim',clim,'nocolorbar'); title (sprintf('Spectogram of output signal: \n Time-variant system applied on exponential sweep'),'Fontsize',14); set(get(gca,'XLabel'),'Fontsize',14); set(get(gca,'YLabel'),'Fontsize',14); subplot(2,2,3); sgram(real(Gs1),'tfr',10,'clim',clim,'nocolorbar'); title (sprintf('Spectogram of output signal: \n Best approximation by Gabor multipliers applied on sinusoid'),'Fontsize',14); set(get(gca,'XLabel'),'Fontsize',14); set(get(gca,'YLabel'),'Fontsize',14); subplot(2,2,4); sgram(real(Ge1),'tfr',10,'clim',clim,'nocolorbar'); title (sprintf('Spectogram of output signal: \n Best approximation by Gabor multipliers applied on exponential sweep'),'Fontsize',14); set(get(gca,'XLabel'),'Fontsize',14); set(get(gca,'YLabel'),'Fontsize',14); ```