hw3 soln

# hw3 soln - Dr Behnaam Aazhangl ELEC 430 Department of...

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Dr. Behnaam Aazhangl ELEC 430 Department of Electrical and Computer Engineering Rice University Due 31 Jan 2008 HOMEWORK 3 — Random Processes II Exercise 1. Sampling Random Processes A discrete-time stochastic process Y n X nT is obtained by periodic sampling of a continuous- time zero-mean stationary process X t where T is the sampling interval, i.e. f s = 1 T is the sampling rate. (a) Determine the relationship between the autocorrelation function of X t and the autocor- relation sequence of Y n . (b) Express the power density spectrum of Y n in terms of the power density spectrum of X t . (c) Determine the conditions under which the power density spectrum of Y n is equal to that of X t . Exercise 2. Processing Gaussian Noise Suppose that white Gaussian noise X t is the input to a linear system with a transfer function deﬁned by H ( f ) = ± 1 | f | ≤ 2 0 | f | > 2 Suppose further that the input process is zero mean and has spectral height N o 2 = 5. Let Y t denote the resulting output process.

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hw3 soln - Dr Behnaam Aazhangl ELEC 430 Department of...

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