PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 509

stem (nn,f1nn)

ylabel (‘Amplitude of f1(n)’);xlabel (‘time index n’);

title(‘f1(n) vs. n’)

axis ([-4 10 0 1.1])

subplot (2,1,2)

f2nn =[zeros(1,4) f2];

stem(nn,f2nn)

title(‘f2(n) vs. n’)

ylabel (‘Amplitude of f2(n)’);

xlabel (‘time index n’); axis([-4 10 0 1.1])

W=linspace(-pi,pi,100);

DTFT _ f1=1./(1-0.3*exp(-j.*W));

DTFT _ f2=1./(1-0.9*exp(-j.*W));

figure(2)

subplot (2,1,1)

plot (W,abs(DTFT _ f1));title(‘ DTFT[f1(n)]=1./(1-0.3*exp(-j.*W))’);

xlabel (‘frequency W ’), ylabel(‘Magnitude’)

subplot (2,1,2)

plot (W,angle(DTFT _ f1));

xlabel (‘frequency W’), ylabel(‘Phase angle in rad.’)

figure(3)

subplot (2,1,1)

plot (W,abs(DTFT _ f2));title(‘ DTFT[f2(n)]=1./(1-0.9*exp(-j.*W))’);

xlabel(‘frequency W ’), ylabel(‘Magnitude’)

subplot(2,1,2)

plot (W,angle(DTFT _ f2));

xlabel (‘frequency W ’), ylabel(‘Phase angle in rad.’)

figure(4)

subplot (2,1,1)

plot (W,real(DTFT _ f1));title(‘ real [DTFT[f1(n)] vs. W’);

ylabel (‘Amplitude’)

subplot (2,1,2)

plot (W,imag(DTFT _ f1));title(‘ imag [DTFT[f1(n)] vs. W’);

xlabel (‘frequency W ’), ylabel(‘Amplitude’)

figure(5)

f12 = 2*f1nn+3*f2nn;

DTFT _ 12 = 2*DTFT _ f1+3*DTFT _ f2;

subplot (3,1,1)

stem(nn,f12);

ylabel (‘Amplitude’)

title (‘[2f1(n)+3f2(n)] vs. time index n’)

subplot (3,1,2)

plot (W,abs(DTFT _ 12)), title(‘abs[DTFT(2f1(n)+3f2(n))] vs. W’);

ylabel (‘Magnitude’)

subplot (3,1,3)

plot (W,angle(DTFT _ 12));title(‘angle[DTFT(2f1(n)+3f2(n))] vs. W’);

ylabel (‘ Phase in rad.’);

xlabel (‘ frequency W’)