Question 11.15.9: Consider the system described by the difference equation y[n...
Consider the system described by the difference equation y[n] = 1.6y[n – 1] – 0.8y[n – 2] + 0.01x[n] + 0.03x[n – 1] + 0.015x[n – 2] with zero initial conditions. Compute and plot the response y[n] of the system to the input signal x[n] when
a. x[n] is the unit impulse sequence δ[n].
b. x[n] is the unit step sequence u[n].
c. x[n] is the unit ramp sequence r[n] (in two ways).
num=[.01 0.03 0.15];
den=[1 -1.6 0.8];
printsys(num,den,'z')
The system transfer function H(z) is \frac{0.01z^\wedge 2\ +\ 0.03z\ +\ 0.15}{z^\wedge 2\ -\ 1.6z\ +\ 0.8}
a.
num=[.01 0.03 0.15];
den=[1 -1.6 0.8];
k=0:60;
y1=dimpulse(num,den,k);
stairs(k,y1)
title('Impulse Response')
b.
y2=dstep(num,den,k);
stairs(k,y2)
title('Step Response')
c1.
ramp=k;
y31=filter(num,den,ramp);
stairs(k,y31);
title('Ramp Response');
c2.
y32=dlsim(num,den,ramp);
stairs(k,y32);
title('Ramp Response');
