Determine the output this lti system input

LINEAR SYSTEMS AND SIGNALS — Ph.D. Qualifying Exam Fall 2011

(i) (7 pts.)

Determine the output when the input to this system is

x(t) = cos(t) + u(t)

x[n] = δ[n] + δ[n − 1] and the output signal is:

y[n] = δ[n − 1] + 3δ[n − 2] + δ[n − 3]
Then, the impulse response h[n], which yields y[n] from x[n] through y[n] = h[n] ∗ x[n] is h[n] = δ[n − 1] + 2δ[n − 2]