Consider the DSB-SC signal s (t) = Ac cos (2πA?ct) m (t)

Consider the DSB-SC signal s (t) = Ac cos (2pA?ct) m (t), where Ac cos (2pA?ct) is the carrier wave and m (t) is the message signal. This modulated signal is applied to a square-law device characterized by y (t) = s2 (t). The output y (t) is next applied to a narrowband filter with a pass-band magnitude response of one, mid-band frequency 2A?c, and bandwidth ?A?. Assume that ?A? is small enough to treat the spectrum of y (t) as essentially constant inside the pass-band of the filter.
(a) Determine the spectrum of the square-law device output y (t).
(b) Show that the filter output v (t) is approximately sinusoidal, given by v (t) = A2c/2 E ?A? cos (4pA?ct), where E is the energy of the message signal m (t).