Question
A digital filter with impulse response $h(n)=0.7^n u(n)$ is excited by white Gaussian noise of zero mean and unit variance. Determine the mean and variance of the output of the digital filter in closed-form during the transient and steady state.
Step 1
During the transient state, the output of the digital filter can be calculated using the convolution sum: $$y(n) = \sum_{k=0}^{n} h(k)x(n-k)$$ where $x(n)$ is the input white Gaussian noise signal. Show more…
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