# Discrete signals and systems problems

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.

https://brainmass.com/engineering/electronic-engineering/discrete-signals-and-systems-problems-604930

#### Solution Summary

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.