PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

554 Practical MATLAB® Applications for Engineers

Example 5.18

Evaluate by hand the transfer function of the difference equation of Example 5.17, given

by g(n) = 0.5g(n − 1) + 2f(n), and then create the script fi le step_imp that returns the

coeffi cients of discrete-step and impulse responses using system simulates and the

MATLAB commands dstep and impz, respectively. Also verify that the solutions obtained

(Example 5.17) fully agree with the solutions obtained using the MATLAB commands

by evaluating the cumulative errors by comparing the two methods.

ANALYTICAL Solution

g(n) − 0.5g(n − 1) = 2f(n)

G(z)[1 − 0.5z−^1 ] = 2F(z)

Hz

Gz

Fz z

()

()

().





 

2

1051

MATLAB Solution

% Script file: step _ imp

num = [0 2];

den = [1 -0.5];

nn = 16;

figure(2)

subplot(2,1,1)

dstep(num,den)

subplot(2,1,2)

impz(num,den)

nnn = 0:10;

[Y,X] = dstep(num,den); [YY,XX] = impz(num,den);

a = gnstep(6:16);b =(Y(2:12))’;error _ step=a-b;

c =hn(6:16);d=(YY(2:12))’;error _ imp=c-d;

disp(‘**********************************************************’)

disp(‘*********************R E S U L T S***********************’)

disp(‘**********************************************************’)

disp(‘ The first 11 coefficients of the step response’)

disp(‘using the simulation of the difference equation are :’)

a

disp(‘using the command dstep are :’)

b

disp(‘ The first 11 coefficients of the impulse response’)

disp(‘using the simulation of the difference equation are :’)

c

disp(‘using the command impz are :’)

d

disp(‘ The cumulative step error [a-b] is :’)

sum(error _ step)

disp(‘ The cumulative impulse error [c-d] is :’)

sum(error _ imp)

disp(‘**********************************************************’)

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