Impulse-Response-and-LTI-Systems---Part-II

A signal $x[n] = \cos(\pi n/4)0.8^n u[n]$ is applied to an LTI system and produces an output $3u[n]$. What output is produced by an input $z[n] = 2x[n-3]$?

An LTI system has impulse response $h[n] = 0.5^nu[n]$. What input $x[n]$ will produce an output $y[n] = 3(0.5)^{(n-1)}u[n-1]$?

An LTI system with impulse response $h[n] = u[n]$ is BIBO stable.

LTI systems 1, 2, and 3 have impulse responses $h_1[n], h_2[n]$ and $h_3[n]$, respectively and are interconnected as follows. The input $x[n]$ is first applied to system 1, then the output of system 1 is applied to systems 2 and 3 arranged in parallel, and the outputs of systems 2 and 3 are summed to produce the output $y[n]$. We seek an expression for the impulse response $h[n]$ of the overall system relating $x[n]$ to $y[n]$. Select all correct answers.