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Exercise 4: Consider the LTI system y(n) = 1.2y(n - 1) - 0.85y(n - 2) + w(n), where $w(n)$ is a zero-mean white noise sequence with unit variance $\sigma^2 = 1$. a) Compute the impulse response $h(n)$ for $0 \le n \le 30$. b) Compute and the output $y(n)$ for $0 \le n \le 100$. c) Compute $r_{yw}(l)$, the input-output crosscorrelation sequence, and compare it with $h(n)$. d) Compute and plot the autocorrelation sequence $r_{ww}(l)$. e) Repeat the experiment 50 times, compare the average crosscorrelation of 50 trials with $h(n)$. f) Justify your observations. Hint: Recall that $r_{yw}(l) = r_{ww}(l) \ast h(l)$.

          Exercise 4: Consider the LTI system
y(n) = 1.2y(n - 1) - 0.85y(n - 2) + w(n),
where $w(n)$ is a zero-mean white noise sequence with unit variance $\sigma^2 = 1$.
a) Compute the impulse response $h(n)$ for $0 \le n \le 30$.
b) Compute and the output $y(n)$ for $0 \le n \le 100$.
c) Compute $r_{yw}(l)$, the input-output crosscorrelation sequence, and compare it with $h(n)$.
d) Compute and plot the autocorrelation sequence $r_{ww}(l)$.
e) Repeat the experiment 50 times, compare the average crosscorrelation of 50 trials with $h(n)$.
f) Justify your observations.
Hint: Recall that $r_{yw}(l) = r_{ww}(l) \ast h(l)$.

Exercise 4: Consider the LTI system
y(n) = 1.2y(n - 1) - 0.85y(n - 2) + w(n),
where w(n) is a zero-mean white noise sequence with unit variance σ^2 = 1.
a) Compute the impulse response h(n) for 0 ≤ n ≤ 30.
b) Compute and the output y(n) for 0 ≤ n ≤ 100.
c) Compute ryw(l), the input-output crosscorrelation sequence, and compare it with h(n).
d) Compute and plot the autocorrelation sequence rww(l).
e) Repeat the experiment 50 times, compare the average crosscorrelation of 50 trials with h(n).
f) Justify your observations.
Hint: Recall that ryw(l) = rww(l) ∗ h(l).

Added by Stephanie A.

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