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A parallel RLC network is driven by an input current source of is white, WSS noise with zero-mean. The output is the voltage across the network. The phase is a random variable uniformly distributed over
(a) Find the output power spectrum by first computing the output autocorrelation function and then transforming.
(b) Check the result of part (a) by using (11.12c).
(c) Determine the output SNR and optimize the bandwidth to maximize the SNR. Assume differs from the center frequency of the RLC filter.
Hints: You may have to calculate the autocorrelation function as a function of and and then let go to infinity to find the steady-state output. There are several conditions you may want to consider; for example, the filter may be overdamped, critically damped, or under damped. It may also have an initial voltage on the capacitor and a current through the inductor. State your assumption about these conditions.
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