PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 553

MATLAB Solution

% Script file: diff _ eq _ res

gnpast _ step =0; m=1;

for n =0:15;

gnstep(m) = 0.5*gnpast _ step+2*1;

gnpast _ step = gnstep(m);

m = m+1;

end

gnstep = [zeros(1,5) gnstep];

figure(1)

subplot(2,1,1)

mm =-5:1:15;

stem(mm,gnstep);title(‘Simulation of step response’)

xlabel(‘time index n’);ylabel(‘Amplitude’),axis([-5 10 0 4.3])

subplot(2,1,2)

dirack=1;h _ past=0;k=1;

for n =0:15;

hn(k) = 0.5*h _ past + 2*dirack;

dirack = 0;

h _ past = hn(k);

k = k+1;

end;

hn = [zeros(1,5) hn];

stem(mm,hn)

xlabel(‘time index n’);ylabel(‘Amplitude’);axis([-5 10 0 2.1])

title(‘Simulation of impulse response’)

The script fi le diff_eq_res is executed, and the simulated results are shown in Figure 5.65.

>> diff _ eq _ res

− 5 0 5 10

0

2

4

Simulation of step response

time index n

Amplitude

− 5 0 5 10

0

1

2

time index n

Amplitude

Simulation of impulse response

FIGURE 5.65

Simulation plots of system step and impulse responses of Example 5.17.