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explore_fsstmt.m
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explore_fsstmt.m
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%% preparation
close all;clc;
clearvars
path(pathdef);
addpath(genpath(strcat(pwd, '/utils')), path);
scrsz = get(groot,'ScreenSize');
%% set up parameters
Fs = 200;
T = 4;
MT = 4;
tSamples = (1/Fs:1/Fs:T)';
N = length(tSamples);
FreqBounds = [0,0.5];
FreqRes = 1e-4;
%% generate random signal using the model in Conceft paper
initstate(1);
% am1 = smooth(cumsum(randn(N,1)) ./ Fs, 200, 'loess');
% am1 = 2 + am1 ./ max(abs(am1));
% am2 = smooth(cumsum(randn(N,1)) ./ Fs, 200, 'loess');
% am2 = 2 + am2 ./ max(abs(am2));
% am1(1:500) = 0;
% am2(end-600:end) = 0;
%
% if1 = smooth(cumsum(randn(N,1)) ./ Fs, 400, 'loess');
% if1 = 10 + 6 * if1 ./ max(abs(if1));
% if2 = smooth(cumsum(randn(N,1)) ./ Fs, 300, 'loess');
% if2 = pi + 3 * if2 ./ max(abs(if2));
% phi1 = cumsum(if1) / Fs;
% phi2 = cumsum(if2) / Fs;
%
% s1 = am1 .* cos(2*pi*phi1);
% s2 = am2 .* cos(2*pi*phi2);
% clean = s1 + s2;
%
% if1(1:500) = nan;
% if2(end-600:end) = nan;
% am1(1:500) = nan;
% am2(end-600:end) = nan;
%
% sigma = 1;
% noise = random('T',4,N,1);
% noise = sigma * noise;
% fprintf('var(noise) = %f\n', var(noise));
% snrdb = 20 * log10(std(clean)./std(noise));
% fprintf('snrdb = %f\n',snrdb);
am1 = smooth(cumsum(randn(N,1)) ./ Fs, 200, 'loess');
am1 = 2 + am1 ./ max(abs(am1));
% am1 = mean(am1) * ones(size(am1));
% am1 = 100*ones(N,1);
if1 = 50*ones(N,1);
% if1 = smooth(cumsum(randn(N,1)) ./ Hz, 400, 'loess');
% if1 = 20 + 6 * if1 ./ max(abs(if1));
% if1 = linspace(5,100,N)';
% if1 = 50-(linspace(sqrt(0),sqrt(50),N).^2)';
phi1 = cumsum(if1) / Fs;
s1 = am1 .* cos(2*pi*phi1);
clean = s1;
sigma = 1;
noise = random('T',4,N,1);
noise = sigma * noise;
fprintf('var(noise) = %f\n', var(noise));
snrdb = 20 * log10(std(clean)./std(noise));
fprintf('snrdb = %f\n',snrdb);
xm = clean + noise;
targetSig = clean;
% plot(targetSig);
%% SST-CWT
tic;
[sstmtResult, instFreqTic, sstmtCell, stftcfsCell, phasetfCell, stftfreqCell] = fsstmt(targetSig, MT, Fs, 'hermite',...
'ExtendSignal', false,...
'WindowParameters', struct('NumPts',377,'HalfWinSpt',10),...
'FreqBounds', FreqBounds*Fs, 'FreqRes', FreqRes*Fs);
toc;
%% visualize phase plots
hq = figure('Position',[scrsz(1) scrsz(2) scrsz(3) scrsz(4)]);
% segIdx = 1:N;
% segIdx = 201:1400;
segIdx = 100:700;
% [~,yAxisHigh] = min(abs(stftfreqCell{1}*Fs-20));
% yAxisIdx = yAxisHigh:length(stftfreqCell{1});
yAxisIdx = 1:length(stftfreqCell{1});
for k = 1:MT
subplot(ceil(MT/2),2,k);
itvPS = abs(Fs*sstmtCell{k}/2).^2;
itvPS_logscale = qclamp(log(1+itvPS), 0.001);
drawObj = itvPS_logscale(yAxisIdx,segIdx);
% drawObj = sstmtCell{k}(yAxisIdx,segIdx);
% drawObj = stftcfsCell{k}(yAxisIdx,segIdx);
mask = abs(stftcfsCell{k}(yAxisIdx,segIdx));
mask = mask > 0;
% mask = mask > mean(mask(:)+0.5*std(mask(:)));
pcolor(tSamples(segIdx), (stftfreqCell{k}(yAxisIdx)), abs(drawObj).*mask);
% pcolor(tSamples(segIdx), (stftfreqCell{k}(yAxisIdx)), angle(drawObj).*mask);
title(sprintf('Hermite Function $k$=%d', k), 'Interpreter', 'latex', 'fontsize', 20);
% phaseTransPlot = phasetfCell{k}(yAxisIdx,segIdx)/(2*pi);
% phaseTransPlot(phaseTransPlot < 0) = 0;
% phaseTransPlot(abs(phaseTransPlot) > 1) = 0;
% % cwtcfsPhasePlot = angle(cwtcfsCell{k}(yAxisIdx,segIdx));
% % cwtcfsPhasePlot(phaseTransPlot < 0 | abs(phaseTransPlot) > 0.2) = 0;
% phasePlotLogVals = log(1+log(1+phaseTransPlot));
% % phaseTransPlot(phasePlotLogVals > mean(phasePlotLogVals(:)+std(phasePlotLogVals(:)))) = 0;
% % pcolor(tSamples(segIdx), cwtfreqCell{k}*Fs, log(1+log(1+phasePlot)));
% pcolor(tSamples(segIdx), (cwtfreqCell{k}(yAxisIdx))*Fs, phaseTransPlot);
% % pcolor(tSamples(segIdx), (cwtfreqCell{k}(yAxisIdx))*Fs, cwtcfsPhasePlot);
% axis([6.5,11.5,6,14]);
shading interp;
colormap(1-gray);
% hold on
% plot(tSamples(segIdx), if1(segIdx), 'r', 'linewidth', 1);
% plot(tSamples(segIdx), if2(segIdx), 'b', 'linewidth', 1);
end
% % hq = figure('Position',[scrsz(1) scrsz(2) scrsz(3) scrsz(4)]);
% segIdx = 201:1400;
% % segIdx = 1:N;
% [~,yAxisHigh] = min(abs(stftfreqCell{1}*Fs-20));
% yAxisIdx = yAxisHigh:length(stftfreqCell{1});
% for k = 1:MT
% subplot(ceil(MT/2),2,k);
% itvPS = abs(Fs*sstmtCell{k}/2).^2;
% itvPS_logscale = qclamp(log(1+itvPS), 0.005);
% pcolor(tSamples(segIdx), instFreqTic, itvPS_logscale(:,segIdx));
% shading interp;
% colormap(1-gray);
% % hold on
% % plot(tSamples(segIdx), if1(segIdx), 'r', 'linewidth', 1);
% % plot(tSamples(segIdx), if2(segIdx), 'b', 'linewidth', 1);
% title(sprintf('Hermite Function $k$=%d', k), 'Interpreter', 'latex', 'fontsize', 20);
% end
% for k = 1:MT
% figure;
% % subplot(ceil(MT/2),2,k);
% % phaseTransPlot = phasetfCell{k}(yAxisIdx,segIdx)/(2*pi);
% % phaseTransPlot(phaseTransPlot < 0) = 0;
% % phaseTransPlot(abs(phaseTransPlot) > 1) = 0;
% cwtcfsPhasePlot = angle(stftcfsCell{k}(yAxisIdx,segIdx));
% % cwtcfsPhasePlot(phaseTransPlot < 0 | abs(phaseTransPlot) > 0.2) = 0;
% % phasePlotLogVals = log(1+log(1+phaseTransPlot));
% % phaseTransPlot(phasePlotLogVals > mean(phasePlotLogVals(:)+std(phasePlotLogVals(:)))) = 0;
% % pcolor(tSamples(segIdx), cwtfreqCell{k}*Fs, log(1+log(1+phasePlot)));
% % pcolor(tSamples(segIdx), (cwtfreqCell{k}(yAxisIdx))*Fs, phaseTransPlot);
% pcolor(tSamples(segIdx), (stftfreqCell{k}(yAxisIdx))*Fs, cwtcfsPhasePlot);
% % axis([6.5,11.5,6,14]);
% axis([2,5,0,8]);
% shading interp;
% colormap(1-gray);
% hold on
% plot(tSamples(segIdx), if1(segIdx), 'r', 'linewidth', 1);
% plot(tSamples(segIdx), if2(segIdx), 'b', 'linewidth', 1);
% title(sprintf('Morse Wavelet $k$=%d', k-1), 'Interpreter', 'latex', 'fontsize', 20);
% % print(sprintf('./result/zebra%03d', k-1), '-djpeg');
% end
%% save all images
% mtarray = cat(3,sstmtCell{:});
% segIdx = 201:1400;
% figure('Position',[scrsz(1) scrsz(2) scrsz(3)/2 scrsz(4)/2]);
% for j=1:size(mtarray,3)
% itvPSmt = abs(Fs*(sum(mtarray(:,segIdx,1:j),3) / j).^2);
% itvPS_logscale = qclamp(log(1+itvPSmt), 0.001);
% pcolor(tSamples(segIdx), instFreqTic, itvPS_logscale);
% shading interp;
% colormap(1-gray);
% xlabel('Time (sec)', 'Interpreter', 'latex', 'fontsize', 20);
% ylabel('Frequency (Hz)', 'Interpreter', 'latex', 'fontsize', 20);
% title(sprintf('SST-CWT-MT, MT=%d', j), 'Interpreter', 'latex', 'fontsize', 20);
% print(sprintf('./result/MT%03d', j), '-djpeg');
% end
%% save results for each orthogonal wavelet
% segIdx = 201:1400;
% mtarray = cat(3,sstmtCell{:});
% figure('Position',[scrsz(1) scrsz(2) scrsz(3)/2 scrsz(4)/2]);
% for j=1:size(mtarray,3)
% itvPSmt = abs(Fs*mtarray(:,segIdx,j).^2);
% itvPS_logscale = qclamp(log(1+itvPSmt), 0.001);
% pcolor(tSamples(segIdx), instFreqTic, itvPS_logscale);
% shading interp;
% colormap(1-gray);
% xlabel('Time (sec)', 'Interpreter', 'latex', 'fontsize', 20);
% ylabel('Frequency (Hz)', 'Interpreter', 'latex', 'fontsize', 20);
% title(sprintf('SST-CWT, Morse Wavelet k=%d', j-1), 'Interpreter', 'latex', 'fontsize', 20);
% print(sprintf('./result/Morse%03d', j-1), '-djpeg');
% end
%% visualize and compare SST results
% segIdx = 201:1400;
% itvPS = abs(Fs*sstmtResult(:,segIdx)/2).^2;
% itvPS_logscale = qclamp(log(1+itvPS), 0.001);
%
% hq = figure('Position',[scrsz(1) scrsz(2) scrsz(3) scrsz(4)]);
%
% pcolor(tSamples(segIdx), instFreqTic, itvPS_logscale);
% shading interp;
% colormap(1-gray);
% % axis([0 inf FreqBounds(1)*Fs FreqBounds(2)*Fs]);
% xlabel('Time (sec)', 'Interpreter', 'latex', 'fontsize', 20);
% ylabel('Frequency (Hz)', 'Interpreter', 'latex', 'fontsize', 20);
% title('SST-CWT', 'Interpreter', 'latex', 'fontsize', 20);
% hold on
% plot(tSamples(segIdx), if1(segIdx), 'r', 'linewidth', 1);
% plot(tSamples(segIdx), if2(segIdx), 'b', 'linewidth', 1);