A parallel RLC network is driven by an input current source of X (t) = A sin (ω ct + θ) + N (t), where is white, WSS noise with zero- mean. The output is the voltage across the network. The phase is a random variable uniformly distributed over [0, 2π].
(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 ωc differs from the center frequency of the RLC filter.