一维时间序列信号的广义傅里叶族变换（Matlab）

广义傅里叶族变换是一种时频变换方法，傅里叶变换、短时傅里叶变换、S变换和许多小波变换都是其特殊情况，完整代码及子函数如下，很容易读懂：

% Run a demo by creating a signal, transforming it, and plotting the results
	
	% Create a fake signal
	N = 256;
	x = linspace(0,1,N);
	sig = zeros(1,length(x));

	% signal example 1 (a single delta)
	sig(N/2) = 1.0;

	% signal example 2 (a mixture of sinusoids and a delta)
	% sig(1:N/2) += (sin((N/16)*2*pi*x)*1.0)(1:N/2);
	% sig(N/2+1:N) += (cos((N/8)*2*pi*x)*1.0)(N/2+1:N);
	% sig(2*N/16+1:3*N/16) += (sin((N/4)*2*pi*x)*1.0)(2*N/16+1:3*N/16);
	% sig(N/2+N/4+1) = 2.0;

	% Do the transform
	partitions = octavePartitions(N);
	windows = boxcarWindows(partitions);
	SIG = GFT(sig,partitions,windows);

	% Interpolate to get a spectrogram
	% The third and fourth parameters set the time and frequency axes respectively,
	% and can be changed to raise or lower the resolution, or zoom in on
	% a feature of interest
	spectrogram = interpolateGFT(SIG,partitions,1024,1024);

	% Display
	figure();
	subplot(3,1,1);
	plot(x,sig,'DisplayName','signal');
	legend('Location','northeast')
	ax = subplot(3,1,2);
	hold on;
	for p = partitions
	    line([x(p),x(p)],[0,max(abs(SIG))],'Color