1. Compute the unit-pulse response h[n] for n=0, 1, 2 for the discrete time system
y[n+2] + 1/2y[n+1] + 1/4y[n] = x[n+1] - x[n]
2. Determine if each of the following signals is periodic. If a signal is periodic, what is its period?
x[n] = 3sin(100n)
x[n] = 4cos(1.5πn)
3. For the discrete signals defined as the following:
x[0] = 4, x[1] = 1, x[3] = -1, x[n] = 0 for all other integers n.
v[0] = 1, v[1] = -2, v[2] = 3, v[3] = -4, v[n] = 0 for all other integers n.
Compute the convolution x[n]*v[n] for n ≥ 0.