The input to a filter is a discrete- time, zero- mean, random process whose autocorrelation function is
RXX [n] = | a | n,
for some constant a such that |a| <1. We wish to filter this process so that the output of the filter is white. That is, we want the output, Y [k], to have an autocorrelation function, RYY [n] = δ[n].
(a) Find the transfer function of the filter. You may express your answer in terms of either a DTFT or a z- transform.
(b) Find the impulse response of the filter. For both parts, make sure your answer results in a causal filter.