PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 531

MATLAB Solution

% Script file: shift

N=256; fs = 8000;Ts =1/fs; shift =32;

t = linspace(0,Ts*255,256);

window = [zeros(1,64) ones(1,64) zeros(1,64) ones(1,64)];

f = 7*cos(2*pi*1000*t);fn=f.*window;

DFT _ fn = fft(fn,256);

fn _ shift = 7*cos(2*pi*1000*(t-shift).*window);

DFT_fn_shift = fft(fn_shift,256);

figure(1)

subplot (3,1,1); % analysis of f(n) = 7cos(2.pi.1000.t)*window

plot (t,fn); ylabel(‘Magnitude’);

title (‘f(n) = 7cos(2.pi.1000.n)*window, analyzed in the time and

frequency domains’)

subplot (3,1,2)

W= [1:1:N/2].*fs/N;

DFT _ mag = abs(DFT _ fn);

DFT _ phase = angle(DFT _ fn);

DFT _ mage = DFT _ mag(1:1:128);

DFT _ phasee = DFT _ phase(1:1:128);

plot(W,DFT _ mage); ylabel(‘abs [ DFT[f(n)]]’);

subplot (3,1,3)

plot (W,DFT _ phasee);

ylabel (‘angle[ DFT [f(n)]]’); xlabel (‘ frequency in Hz’)

figure(2); % Analysis of 7cos(2.pi.(n-shift))

DFT_mags = abs(DFT_fn_shift);

DFT _ phases = angle(DFT _ fn _ shift);

DFT _ magess = DFT _ mag(1:1:128);

DFT _ phasess =DFT _ phase(1:1:128);

subplot (3,1,1)

plot (t,fn _ shift);

title(‘ f(n-32) analyzed in the time and frequency domains’)

ylabel(‘Amplitude in time’);

subplot(3,1,2)

plot(W,DFT _ magess);

ylabel(‘Magnitude DFT[f(n-32)]’);

subplot(3,1,3)

plot(W,DFT _ phasess);

xlabel(‘frequency in Hz ’); ylabel(‘Phase of DFT[f(n-32)]’);

figure(3) % error analysis

subplot(3,1,1)

error _ time = fn-fn _ shift;

plot(t, error _ time);

title(‘ Error analysis in the time and frequency domains ’)

ylabel(‘Magnitude in time’)

subplot(3,1,2)

error _ mag=abs(DFT _ fn)-abs(DFT _ fn _ shift);

b a r(W,a b s(er r or _ m ag(1:128)));yla b el(‘M ag n itu d e ’);

subplot(3,1,3)

error _ phase=angle(DFT _ fn)-angle(DFT _ fn _ shift);

bar(W,abs(error _ phase(1:128)));ylabel(‘Phase ’);