Question

If a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, then what is the scaled spectrum?

(a) X(F)

(b) Fs.X(F)

(c) X(F)/Fs

(d) None of the mentioned

This question was posed to me in unit test.

Question is from IIR Filter Design by Impulse Invariance in chapter Digital Filters Design of Digital Signal Processing

Answer 1

Correct option is (b) Fs.X(F)

For explanation: When a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is periodic repetition of the scaled spectrum Fs.X(F).