The receiver of an AM system consists of a band-pass filter, a demodula-tor, and a low-pass filter. The received signal is

r(t) = m(t)cos(40000π t) + q(t)

where m(t) is a desired voice signal with bandwidth BW = 5 KHz that modulates the carrier cos(40000π t) and q(t) is the rest of the signals available at the receiver outside the band where the message is. The low-pass filter is ideal with magnitude 1 and bandwidth BW. Assume the band-pass filter is also ideal and that the demodulator is cos(Ω_ct).

(a) What is the value of ­cin the demodulator?

(b) Suppose we input the received signal into the band-pass filter cascaded with the demodulator and the low-pass filter, determine the magnitude response of the band-pass filter that allows us to recover m(t). Draw the overall system and indicate which of the components are LTI and which are LTV.

(c) By mistake we input the received signal into the demodulator, and the resulting signal into the cascade of the band-pass and the low-pass filters. If you use the bandpass filter obtained above, determine the recovered signal (i.e., the output of the low-pass filter). Would you get the same result regardless of what m(t) is? Explain.