PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

542 Practical MATLAB® Applications for Engineers

g. Estimate and plot (Figure 5.59) the magnitude and phase errors of the two methods

in the frequency domain defi ned by the following relations:

mag_error = abs{fft[gf (n)]} − abs{fft[gc(n)]}

phase_error = angle{fft[gf (n)]} − angle{fft[gc(n)]}

over the range 1 ≤ k ≤ 50.

The MATLAB solution for Example 5.13 is given by the script fi le discrete_syst as

follows:

ANALYTICAL Solution

Part a

g(n) = 0.7g(n − 1) − 0.3g(n − 2) + f(n) + 0.9f(n − 1)

g(n) − 0.7g(n − 1) + 0.3g(n − 2) = f(n) + 0.9f(n − 1)

Taking the ZT yields

G(z) − 0.7z−^1 G(z) + 0.3z−^2 G(z) = F(z) + 0.9z−^1 F(z)

G(z)[1 − 0.7z−^1 + 0.3z−^2 ] = F(z)[1 + 0.9z−^1 ]

Hz

z

zz

()










109

107 03

1

12

.

..

Part b

Replacing z = ejW

He

Ge

Fe

e

ee

jW jW

jW

jW

() jW j W

()

()

.

..













109

107 032

MATLAB Solution

% Script file: discrete _ syst

num = [1 0.9];

den = [1 -0.7 0.3];

n = 1:1:50;

fn = 0.9.^n.*sin(0.033*pi.*n);

gnf = filter(num,den,fn);

figure(1) % input and output plots

subplot(2,1,1)

plot(n,fn,’o’,n,fn);

title(‘[System input sequence f(n)] vs n’)

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

subplot(2,1,2)

plot(n,gnf,’s’,n,gnf);