1. A discrete-time system is described by the following difference equation
y[n]=1.15y[n-1]-1.5y[n-2]+0.7y[n-3]-0.25y[n-4]+0.18x[n] +0.1x[n-1]+0.3x[n-2]+0.1x[n-3]+0.18x[n-4] with zero initial conditions.
(a) Compute and plot the impulse response h[n],0= n = 100 using the function h=impz(b,a,N).
(b) Compute and plot the output y[n], ifx[n]=u[n],0= n=100 using the function y=filter(b,a,x).
(c) Compute and plot the output y[n], ifx[n]=u[n],0= n=100 using the function y=conv(h,x).
(d) Compute and plot the output y[n], ifx[n]=u[n],0= n=100 using the function y=filter(h,1,x). Compare and explain the obtained results