Repost Correction part a its xn 05n un please solve all t

Repost:

Correction; part a . it\'s x[n] = (-0.5)^n (u(n) )

please solve all the parts ... and explanin

For the FIR filter y[n] = x[n]-ax[n-1], determine the output signal y[n] for two similar cases. IR filter yin] - xin]-axin-1, determine the ou (a) The infinite-length input signal x[n] = anu[n] (b) The length-8 input signal x[n] = an(u[n]-u[n-8). (c) For part (b), plot x[n] and yIn] for Osns 10.

Solution

Y[n]=x[n]-x[n-1]

apply z transform

Y[z]=X[z][1-z^-1]

H[z]=Y[z]/X[Z]=[1-z^-1]

take inverse Z transform

x[n] = (-0.5)^n (u(n) )

X[z]=1/(1+0.5z-1)

Y[Z]=H[Z]X[Z]=[1-z^-1]/[1+0.5z^-1]=

to find y[n] take inverse Z transform:

y[n]=(-0.5ⁿu[n]-0.5ⁿu[n-1])

c)