Question

What is the equivalent time domain relation of xl(t) i.e., lowpass signal?

(a) \(x_l (t)=[x(t)+j ẋ(t)]e^{-j2πF_c t}\)

(b) x(t)+j ẋ(t) = \(x_l (t) e^{j2πF_c t}\)

(c) \(x_l (t)=[x(t)+j ẋ(t)]e^{-j2πF_c t}\) & x(t)+j ẋ(t) = \(x_l (t) e^{j2πF_c t}\)

(d) None of the mentioned

This question was addressed to me in an internship interview.

My question comes from The Representation of Bandpass Signals in portion Sampling and Reconstruction of Signals of Digital Signal Processing

Answer 1

Right answer is (c) \(x_l (t)=[x(t)+j ẋ(t)]e^{-j2πF_c t}\) & x(t)+j ẋ(t) = \(x_l (t) e^{j2πF_c t}\)

The best I can explain: \(x_l (t)=x_+ (t) e^{-j2πF_c t}\)

=\([x(t)+j ẋ(t)] e^{-j2πF_c t}\)

Or equivalently, x(t)+j ẋ(t) =\(x_l (t) e^{j2πF_c t}\).