PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 539

0

0

0.5

1

Amplitude1.5

2

2.5

3

3.5

0.1 0.2 0.3 0.4 0.5 0.6

time

0.7 0.8 0.9 1

[f(t)=3*exp(-5*t)] versus t

FIGURE 5.52

Plot of f(t) over the range 0 ≤ t ≤ 1 of Example 5.12.

axis([-1e4 1e4 0 0.01])

subplot (2,1,2)

plot (W,angle(Fdc));title(‘angle[DFT[f(n)]] vs w’);ylabel(‘Phase’);

xlabel (‘frequency w ’);

figure(3) % analog frequency analysis

F _ table = 3./(5+j*W);

subplot (2,1,1)

absF _ table = abs(F _ table);

plot(W(200:400),absF _ table(200:400));

title(‘abs[FT[f(t)]] vs w’);

ylabel(‘Magnitude’);axis([-.1e4 .1e4 0 0.8]);

subplot (2,1,2)

plot (W,angle(F _ table));title(‘angle[FT[f(t)]] vs w’);ylabel(‘Phase’);

xlabel (‘frequency w ‘);axis([-1e4 1e4 -2 2]);

figure(4) % error analysis in frequency

error _ mag = abs(F _ table)-abs(Fdc);

error _ phase = angle(F _ table)-angle(Fdc);

subplot (2,1,1)

plot (W(200:400) ,error _ mag(200:400));axis([-.2e4 .2e4 0 0.8]);

title (‘error mag.=abs[FT[f(t)]]-abs[DFT[f(n)]] vs w n’);

ylabel (‘Magnitude’); xlabel (‘index n’)

subplot(2,1,2)

bar(W,error _ phase);title(‘error phase=angle[FT[f(t)]-angle[DFT[f(n)]]

vs w’);

ylabel(‘Phase’);xlabel(‘frequency w’);

The script fi le FT_DFT is executed, and the results are as follows:

>> FT _ DFT