Dtermine the approximate output if a bandpass signal xt

Question

Consider the simple RC circuit shown in Fig. P2.3-3. Let R = 1 kΩ and C = 1 nF.

(a) Find the system transfer function.

(b) Plot the magnitude and phase responses.

(c) Show that a lowpass signal x(t) with bandwidth W « 10⁶ will be transmitted practically without distortion. Determine the output.

(d) Determine the approximate output if a bandpass signal x(t) = g(t) cos(ωct) is passed through this filter. Assume that ωc = 3 × 10⁶ and that the envelope g(t) has a very narrow band, on the order of 50 Hz.