# Question

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.

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.

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