% lab 4 presentation
% lcb 10.26.2000

% time vector
fs=44100;                                           % sampling rate  
n=1:fs;                                             % 1 second at sampling rate
display=1:400;                                      % number of samples to display in time domain stem plots

% square wave (x[n] input to filter)
squarecomponent=[ones(1,100), -1.*ones(1,100)];     % make a single period of the square wave
square=[repmat(squarecomponent,1,220) ones(1,100)]; % repeat this period 220.5 times to fill out time vector -> 220.5 Hz frequency at 44.1 kHz srate

% display square wave in the time and frequency domains
figure(1);
subplot(2,1,1);
stem(display,square(display));
subplot(2,1,2);
specgram(square);

soundsc(square,fs);

pause

% first filter: one-zero (lowpass)
b0 = [1 1];                                         % filter coefficients
y0 = firfilt(b0,square);                            % matlab fir filtering function

% display one-zero's output in the time and frequency domains
figure(2);
subplot(2,1,1);
stem(display,y0(display));                          % note that filter output is longer than filter input
subplot(2,1,2);
specgram(y0);                                       % note the relative strength of the high frequencies

soundsc(y0,fs);

pause

% second filter: one-zero with altered coefficients (highpass)
b1 = [1 -1];
y1 = firfilt(b1,square);

% display new one-zero's output in the time and frequency domains
figure(3);
subplot(2,1,1);
stem(display,y1(display));
subplot(2,1,2);
specgram(y1);                 

soundsc(y1,fs);

pause

% third filter: running average (lowpass)
b2 = 1/10.*ones(1,10);
y2 = firfilt(b2,square);

% display running average's output in the time and frequency domains
figure(4);
subplot(2,1,1);
stem(display,y2(display));
subplot(2,1,2);
specgram(y2);

soundsc(y2,fs);

pause

% fourth filter: well-designed lowpass
b3=fir1(96,0.2);                            % order 96 -> long filter; normalized cutoff frequency 0.2
y3 = firfilt(b3,square);

% stem filter coefficients
figure(5);
stem(0:96, b3);

pause

% display filter output in the time and frequency domains

display2=1:200;                             % zoom in a bit in the time domain

figure(6);
subplot(2,1,1);
stem(display2,y3(display2));
subplot(2,1,2);
specgram(y3);

soundsc(y3,fs);                             % scale because filter is outputting values > 1