Chapter 3

% Program 3_1

% Discrete-Time Fourier Transform Computation

%

% Read in the desired number of frequency samples

k = input('Number of frequency points = ');

% Read in the numerator and denominator coefficients

num = input('Numerator coefficients = ');

den = input('Denominator coefficients = ');

% Compute the frequency response

w = 0:pi/(k-1):pi;

h = freqz(num, den, w);

% Plot the frequency response

subplot(2,2,1)

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

title('Real part')

xlabel('\omega/\pi'); ylabel('Amplitude')

subplot(2,2,2)

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

title('Imaginary part')

xlabel('\omega/\pi'); ylabel('Amplitude')

subplot(2,2,3)

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

title('Magnitude Spectrum')

xlabel('\omega/\pi'); ylabel('Magnitude')

subplot(2,2,4)

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

title('Phase Spectrum')

xlabel('\omega/\pi'); ylabel('Phase, radians')

% Program 3_2

% Generate the filter coefficients

h1 = ones(1,5)/5; h2 = ones(1,14)/14;

% Compute the frequency responses

[H1,w] = freqz(h1, 1, 256);

[H2,w] = freqz(h2, 1, 256);

% Compute and plot the magnitude responses

m1 = abs(H1); m2 = abs(H2);

plot(w/pi,m1,'r-',w/pi,m2,'b--');

ylabel('Magnitude'); xlabel('\omega/\pi');

legend('M=5','M=14');

pause

% Compute and plot the phase responses

ph1 = angle(H1)*180/pi; ph2 = angle(H2)*180/pi;

plot(w/pi,ph1,w/pi,ph2);

ylabel('Phase, degrees');xlabel('\omega/\pi');

legend('M=5','M=14');

% Program 3_3

% Set up the filter coefficients

b = [-6.76195 13.456335 -6.76195];

% Set initial conditions to zero values

zi = [0 0];

% Generate the two sinusoidal sequences

n = 0:99;

x1 = cos(0.1*n);

x2 = cos(0.4*n);

% Generate the filter output sequence

y = filter(b, 1, x1+x2, zi);

% Plot the input and the output sequences

plot(n,y,'r-',n,x2,'b--',n,x1,'g-.');grid

axis([0 100 -1.2 4]);

ylabel('Amplitude'); xlabel('Time index n');

legend('y[n]','x2[n]','x1[n]')