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Let X(t) be a weakly stationary process with zero mean, autocorrelation function RXX , and power spectral density SXX(f). We are required to find a linear filter with impulse response h(t), such that the filter output is X(t) when the input is white-noise of power spectral density N0/2.

a. Determine the condition that the impulse response h(t) must satisfy in order to achieve this requirement.

b. What is the corresponding condition on the transfer function H(f) of the filter?

c. Using the Paley-Wiener criterion discussed in Chapter 2, find the requirement on SXX(f) for the filter to be causal.

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Project Management, Management Studies

Category:- Project Management
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