% script for experimenting with FM synthesis
% you can comment various lines in and out and change
% parameters to play with different effects
% Aaron Lanterman, 3/5/08

fs = 44100;
tt = 0:(1/fs):0.5;

wc = 240*2*pi;
wm = 240*2*pi;

%wm = linspace(110*2*pi,2200*2*pi,length(tt));
%wc = linspace(2200*2*pi,110*2*pi,length(tt));
%index = linspace(15,0,length(tt));
%index = linspace(0,10,length(tt));
index = 11;

% yes, it turns out the phase relationship between the 
% carrier and the modulator does matter!
%theta = linspace(0,2*pi,length(tt));
theta = 0;

xx = cos(wc .* tt + index .* sin(wm .* tt + theta)); 
%xx = cos(wc .* tt + index .* cos(wm .* tt)); 
%xx = cos(wc .* tt);
soundsc(xx,fs);

% The FFT will only be clear if you keep the parameters
% constant over time
% By multiplying by 2, I'm plotting a cosine style spectrum
% instead of an complex exponential style spectrum
fftxx = 2 * abs(fft(xx)) / length(xx);
lenx = length(xx);
ff = linspace(0,fs*(lenx-1)/lenx,length(fftxx));

% change the end values of the subsets to plot more or less
% of the FFT
plot(ff(1:4000),fftxx(1:4000));

% The sampling rate 44.1 kHz is too high to see details in 
% the spectrogram since all the lines are squished down at 
% the lower frequestion, so let's downsample the signal
% taking the spectrogram

% xxres = resample(xx,1,4);
% specgram(xxres,1024,fs)