Question

1. Draw frequency domain representations (sketches of the real and imaginary parts of the Fourier transform) for both cos(2*pi*fc*t) and sin(2*pi*fc*t), for a carrier waveform.

____________________

Now suppose we have a sinusoidal signal of frequency fi, where fi << fc. Let the signal be m(t)=cos(2*pi*fi*t) and the carrier be cos(2*pi*fc*t). Say we mix m(t) up to carrier frequency fc when we multiply m(t) by the carrier to create the modulated signal, s(t) = m(t) * cos(2*pi*fc*t).

Draw the real part of the Fourier Transform of s(t). Use the two below approaches:

1. Use the Fourier transforms of m(t) and cos(2*pi*fc*t) and the fact that multiplication in the time domain is convolution in the frequency domain.

2. Use a trigonometric identity to rewrite s(t) in the time domain. Then take the Fourier transform of s(t).

Sketch the real part of the Fourier Transform of s(t) if the real part of the Fourier Transform of m(t) is a symmetric triangle centered at f=0 with a M(0)>0.

Thanks for your help!!!!!

Answer 1

Answer 2