Question

Which of the following is true about the interpolated signal whose spectrum is V(ωy)?

(a) (I-1)-fold non-periodic

(b) (I-1)-fold periodic repetition

(c) I-fold non periodic

(d) I-fold periodic repetition

This question was posed to me during a job interview.

The doubt is from Interpolation by a Factor I in section Digital Filters Design of Digital Signal Processing

Answer 1

Right option is (d) I-fold periodic repetition

Easiest explanation: We observe that the sampling rate increase, obtained by the addition of I-1 zero samples between successive values of x(n), results in a signal whose spectrum is an I-fold periodic repetition of the input signal spectrum.