Digital Signal Processing

Lab 3

Exercise 1

Low pass filter

Fs = 8000;               % Sample everything at 8000 Hz

Fo1 = 660;         % Use 660 Hz as the fundamental freq of each waveform

Fo2 = 3900;         % Use 660 Hz as the fundamental freq of each waveform

T_total = 1.2;           % Compute a total of 1.2 seconds so the sound can be played

tt = 0:(1/Fs):T_total;       % Set up the time axis

% =====  First the cosine  =====

y1 = cos(2*pi*Fo1*tt)+0.5*cos(2*pi*Fo2*tt);

y2 = filter([1], [1 -0.8], y1);

range = 801:880;    % Only plot a part of the signal

figure(1)

subplot(2,1,1)

plot(tt(range),y1(range))

xlabel('TIME (sec)')

title('y1')

%sound(y1, Fs)

subplot(2,1,2)

plot(tt(range),y2(range))

xlabel('TIME (sec)')

title('y2')

H = 0;

w=-pi:pi/500:pi;

for k=1:length(y1)                 % sum(hk exp(-jkw)

      H = H + y1(k)*exp(-j*(k-1)*w);                              

end                              

mag=abs(H);

figure(2)

plot(w,mag)

axis([-pi pi 0 max(mag)])

%

H = 0;

w=-pi:pi/500:pi;

for k=1:length(y2)                 % sum(hk exp(-jkw)

      H = H + y2(k)*exp(-j*(k-1)*w);                              

end                              

mag=abs(H);

figure(3)

plot(w,mag)

axis([-pi pi 0 max(mag)])

Exercise 2

High pass filter

Change the y2  to be

y2 = filter([1 -0.6], [1], y1);

Sources:

Fundamentals of Digital Signal Processing, by Joyce Van de Vegte, Prentice Hall, 2002.