Question

Which of the following is the right way of representation of equation that contains only the positive frequencies in a given x(t) signal?

(a) X+(F)=4V(F)X(F)

(b) X+(F)=V(F)X(F)

(c) X+(F)=2V(F)X(F)

(d) X+(F)=8V(F)X(F)

This question was posed to me in class test.

My question is taken from The Representation of Bandpass Signals in section Sampling and Reconstruction of Signals of Digital Signal Processing

Answer 1

The correct option is (c) X+(F)=2V(F)X(F)

To explain: In a real valued signal x(t), has a frequency content concentrated in a narrow band of frequencies in the vicinity of a frequency Fc. Such a signal which has only positive frequencies can be expressed as X+(F)=2V(F)X(F)

Where X+(F) is a Fourier transform of x(t) and V(F) is unit step function.