The transfer function Gz z3 05z2 025z 0125z4 is an FIR a

The transfer function G(z) = z^3 + 0.5z^2 + 0.25z + 0.125/z^4 is an FIR approximation to the transfer function H(z) = 1/z - 0.5. Plot the step response of each system. Determine the d.c. gain of each system from its step response. Plot the frequency response of each system. Determine the d.c. gain of each system from its frequency response.

Solution

Gnum = [1 0.5 0.25 0.125];
Gden = [1 0 0 0 0];
Hnum=1;
Hden=[1 -0.5];
Ts = 0.1;
Gsys = tf(Gnum,Gden,Ts);
Hsys =tf(Hnum,Hden,Ts);
figure(1)
step(Gsys,Hsys);
legend(\'G(Z)\',\'H(Z)\');
figure(2)
freqz(Gnum,Gden);
hold on
freqz(Hnum,Hden);
legend(\'G(Z)\',\'H(Z)\');