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).
Fig: 1