Question

What is the possible representation of x(t) if xl(t)=a(t)e^(jθ(t))?

(a) x(t) = a(t) cos[2πFct – θ(t)]

(b) x(t) = a(t) cos[2πFct + θ(t)]

(c) x(t) = a(t) sin[2πFct + θ(t)]

(d) x(t) = a(t) sin[2πFct – θ(t)]

This question was posed to me during an online exam.

Question is from The Representation of Bandpass Signals topic in section Sampling and Reconstruction of Signals of Digital Signal Processing

Answer 1

Right option is (b) x(t) = a(t) cos[2πFct + θ(t)]

To explain: x(t) = Re\([x_l (t) e^{j2πF_c t}]\)

= Re\([a(t) e^{j[2πF_c t + θ(t)]}]\)

= \(a(t) \,cos⁡ [2πF_c t+θ(t)]\)

Hence proved.