Discrete-Time Convolution:
1. Find the impulse response for each of the following discrete-time systems:
a) y[n] + 0.2y[n-1] = x[n]-x[n-1]
b) y[n] + 1.2y[n-1] = 2x[n-1]
c) y[n] = 0.24(x[n]+x[n-1]+x[n-2]+x[n-3])
d) y[n] = x[n] + 0.5x[n-1] + x[n-2]
2. Perform the following convolutions, x[n]*v[n]
a) x[n] = u[n] - u[n-4], v[n] = 0.5nu[n]
b) x[n] = [1 4 8 2]; v[n] = [0 1 2 3 4] (the sequences both start at n=0)
c) x[n] = u[n], v[n] = 2(0.8)nu[n]
d) xn un[] [ ]=−1, vn un
n
[] (.) []=205
docsity.com