Question

Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier transform of sy(t). (2.5 points) N(f) df, where Nyf) is the power spectral b. Find the input noise power Pa=S density of input noise. (2.5 points) Hint: Use Parseval's relationship if necessary . What is the input signal-to-noise (SNR,) ratio, defined as: SNRi = 10log1o (25 points) Pnx d. Find the output power spectral density of noise N,(f) N,(f). |H(f,where H is the frequency response of the circuit, and Ng(f) is the power spectral density of the input noise. (2.5 points). e. Determine the output noise power, Pyn Ny (f)df. (2.5 points). f. Compute the output signal power, Py = S( r+oo IH()12 df. (2.5 points). What is the output signal-to-noise (SNRo) ratio, defined as: SNRO = 10log10 (P g. How much SNR improvement has been achieved with this filtering operation ? (2.5 points).

Answer 1

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