2. A signal r(t) is modulated with a carrier signal with frequency fe, but demodulated slightly out of tune with a frequency fc + Afc

What will X(f) and r(t) look like, after suitable filtering? You may solve this by using trigonometric relations like cos(a - b) = cos(a) cos(b) +

sin(a) sin(b) (you can get this all from WolframAlpha). You may also solve this in the frequency domain, by considering:

• The Fourier transform of the product of functions is the convolution of the Fourier transforms of the functions, (you know this in the reverse case)

• That the Fourier transform of the cos function is a sum of delta functions (you knew that),

• The sampling property of delta functions (you know those, too).