% DispChirps.m Script 
% 
% -- display three different kinds of chirp signals 
%    as non-stationary signal 
% 
% -- visual comparison between the Fourier Analysis 
%    and Phase Analysis 
% 

% --------------------------------------------------
% Xiaobai Sun 
% Duke CS 
% For the class of Numerical Analysis and Methods 
% --------------------------------------------------

clear all 
close all 


figid = 0; 

padz = zeros( 10, 1); 

% EXAMPLE 1: Compute the spectrogram of a linear chirp.

t =  0:0.001:2;                    % 2 secs @ 1kHz sample rate
y =  chirp(t,0,1,150);             % Start @ DC, cross 150Hz at t=1sec
yf = fft( y ) ; 

figid = figid  + 1; 
figure( figid ) 

subplot(3,1,1) 
plot( y(1:5:end) ) 
xlabel( 't' )
ylabel( 's(t)' ) 

subplot(3,1,2) 
plot( abs(yf(1:5:end)) ) 
xlabel( 'f' )
ylabel( ' Amplitude |S(f)|' ) 

subplot(3,1,3) 
spectrogram(y,256,250,256,1E3); % Display the spectrogram

title( 'spectrogram of a linear chirp' ) 



%  EXAMPLE 2: Compute the spectrogram of a quadratic chirp.

t=-2:0.001:2;                   % +/-2 secs @ 1kHz sample rate
y=chirp(t,100,1,200,'q');       % Start @ 100Hz, cross 200Hz at t=1se
yf = fft( y ) ; 

figid = figid  + 1; 
figure( figid ) 

subplot(3,1,1) 
plot( y(1:10:end) ) 
xlabel( 't' )
ylabel( 's(t)' ) 

subplot(3,1,2) 
plot( abs(yf(1:5:end)) ) 
xlabel( 'f' )
ylabel( ' Amplitude |S(f)|' ) 

subplot(3,1,3) 

spectrogram(y,128,120,128,1E3); % Display the spectrogram
title( 'Quadratic  chirp' ) 

%    EXAMPLE 3: Compute the spectrogram of a logarithmic chirp
 
t= 0:0.001:10;                   % 10 seconds @ 1kHz sample rate
fo=10;f1=400;                    % Start at 10Hz, go up to 400Hz
y=chirp(t,fo,10,f1,'logarithmic');
yf = fft( y ) ; 

figid = figid  + 1; 
figure( figid ) 

subplot(3,1,1) 
plot( y(1:10:end) ) 
xlabel( 't' )
ylabel( 's(t)' ) 

subplot(3,1,2) 
plot( abs(yf(1:5:end)) ) 
xlabel( 'f' )
ylabel( ' Amplitude |S(f)|' ) 

subplot(3,1,3) 
spectrogram(y,256,200,256,1000); % Display the spectrogram.
title( 'Logrithm  chirp' )