Consider the amplitude modulation system in Fig. P-12.4(a) with a bandlimited input signal...

Consider the amplitude modulation system in Fig. P-12.4(a) with a bandlimited input signal x (t) as

depicted in Fig. P-12.4(b). Assume that the LTI system has the frequency response of an ideal bandpass filter

(a) Plot the Fourier transform H(j ω) of the ideal BPF specified above. Make the plot for both negative and positive frequencies.

(b) Plot the Fourier transform V(j ω) of the signal v (t) at the output of the multiplier.

(c) Plot the Fourier transform Y (j ω) of the output signal y(t) from the filter. Do not try to find y(t).

(d) The output signal is called a “single-sideband” signal. Can you justify this terminology?

Note that the negative frequency portion of the Fourier transform X (j ω) in Fig. P-12.4 (b) is shaded. Mark the corresponding region or regions in your plots of V (j ω) and Y (j ω).