DISCRETE-TIME SIGNALS IN THE FREQUENCY DOMAIN

DISCRETE-TIME SIGNALS IN THE FREQUENCY DOMAIN

Program can be used to evaluate and plot the DTFT of the form of above equation

% Program

% Evaluation of the DTFT

clf;

% Compute the frequency samples of the DTFT

w = -4*pi:8*pi/511:4*pi;

num = [2 1];den = [1 -0.6];

h = freqz(num, den, w);

% Plot the DTFT

subplot(2,1,1)

plot(w/pi,real(h));grid

title(’Real part of H(e^{j\omega})’)

xlabel(’\omega /\pi’);

ylabel(’Amplitude’);

subplot(2,1,2)

plot(w/pi,imag(h));grid

title(’Imaginary part of H(e^{j\omega})’)

xlabel(’\omega /\pi’);

ylabel(’Amplitude’);

pause

subplot(2,1,1)

plot(w/pi,abs(h));grid

title(’Magnitude Spectrum |H(e^{j\omega})|’)

xlabel(’\omega /\pi’);

ylabel(’Amplitude’);

subplot(2,1,2)

plot(w/pi,angle(h));grid

title(’Phase Spectrum arg[H(e^{j\omega})]’)

xlabel(’\omega /\pi’);

ylabel(’Phase, radians’);

Program can be used to verify the convolution property of the DTFT

% Program

% Convolution Property of DTFT

clf;

w = -pi:2*pi/255:pi;

x1 = [1 3 5 7 9 11 13 15 17];

x2 = [1 -2 3 -2 1];

y = conv(x1,x2);

h1 = freqz(x1, 1, w);

h2 = freqz(x2, 1, w);

hp = h1.*h2;

h3 = freqz(y,1,w);

subplot(2,2,1)

plot(w/pi,abs(hp));grid

title(’Product of Magnitude Spectra’)

subplot(2,2,2)

plot(w/pi,abs(h3));grid

title(’Magnitude Spectrum of Convolved Sequence’)

subplot(2,2,3)

plot(w/pi,angle(hp));grid

title(’Sum of Phase Spectra’)

subplot(2,2,4)

plot(w/pi,angle(h3));grid

title(’Phase Spectrum of Convolved Sequence’)