An LTI system has impulse response given by the following plot: The input to th...

An LTI system has impulse response given by the following plot:

The input to the system, x[n], is plotted below as a function of n.

(a) Use discrete convolution to determine the output of the system y[n] = x[n] ∗ h[n] for the above input. Give your answer as a carefully labeled sketch of y[n] over a range sufficient to define it completely.

(b) The deterministic autocorrelation of a signal x[n] is defined in Eq. (2.188) as c_xx[n] = x[n] ∗ x[−n]. The system defined by Figure P2.35-1 is a matched filter for the input in Figure P2.35-2. Noting that h[n] = x[−(n−4)], express the output in part (a) in terms of c_xx[n].

(c) Determine the output of the system whose impulse response is h[n] when the input is x[n] = u[n + 2]. Sketch your answer.