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 = 4, x = 1, x = -1, x[n] = 0 for all other integers n.
v = 1, v = -2, v = 3, v = -4, v[n] = 0 for all other integers n.
Compute the convolution x[n]*v[n] for n ≥ 0.
The solution covers the problems of impulse response, periodicity and convolution for discrete signals and systems which are linear and time-invariant. It contains a detailed step-by-step guide with important calculations and illustrations. Content of the solution is 4 pages long with 690 words and 3 figures.