A simple way to smooth data is to just take a weighted average of a number of samples. Consider an LTI system with input and output related by
y[n] = ax[n – 1] + (1 – a)x[n].
Assume that all initial conditions are 0.
(a) Find the system impulse response h[n].
(b) Find the impulse response of the system needed to recover x[n] from y[n]. (Hint: consider the inverse system.)
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