HW7.3 (Frequency Mismatch in Amplitude Modulation) A bandlimited continuous- time signal x has the triangular spectrum shown below: X(w) -A +A 3 The following diagram shows an amplitude modulation-demodulation scheme to communicate the signal x to a receiver. In this problem, you'll explore the effects r(t) r(t) x(t) ✗ y(t) qR(t) = cos(wit) qr(t) = cos(wot) of frequency mismatch between the transmitter and receiver carriers qr and QR, respectively. In particular, assume that 0<< A < 0 = W₁ + € (a) Determine reasonably simple expressions for the signals r and y. You may find the following trigonometric identity useful: cos a cos = [cos(a + B) + cos(a - ẞ)] (b) Provide well-labeled plots of R(w) and Y(w), the spectra of the signals r and y, respectively. (c) Explain why the information-bearing signal x is irrecoverable, even if we send the signal y through an ideal low-pass filter.