Question

What is the period of the scaled spectrum Fs.X(F)?

(a) 2Fs

(b) Fs/2

(c) 4Fs

(d) Fs

The question was asked during an interview.

My query is from IIR Filter Design by Impulse Invariance in division Digital Filters Design of Digital Signal Processing

Answer 1

The correct answer is (d) Fs

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) with period Fs.