%  ex_rv_1.m  Example to  illustrate frequency analysis of signals
%
% written by Babu Joseph, Washington University, July 2000
%
% First generate a signal containing two sinewaves and white noise
%
t=0:4990;% time vector
t_samp=1;% sample time
N=length(t); % no of sample points
x=sin(t*pi/100)+sin(t*3*pi/100)+rand(1,N);% pi/100 and 3pi/100 are dominant

plot(t,x);
pause
%
% now analyze the spectrum
%
X=fft(x);
% matlab computes frequency range from 2pi/(t_samp) to 2Pi/t_samp
% The transform is symmetric about the nyquist frequency  pi/t_samp
%
% only the first half is necessary.
freq=0:2*pi/(t_samp*N):pi/t_samp;
amp=abs(X(1:N/2+1))*2/N; % Takes the first half and normalizes it so 
% unit amplitude in time corresponds to unit amplitude in frequency
loglog(freq,amp);% use loglog since power varies a great deal