Question

The filter eliminates the spectrum of X(ω) in the range π/D < ω < π.

(a) True

(b) False

This question was posed to me in an interview for internship.

I'd like to ask this question from Decimation by a Factor D topic in section Multirate Digital Signal Procesing of Digital Signal Processing

Answer 1

Correct answer is (a) True

For explanation: The input sequence x(n) is passed through a low pass filter, characterized by the impulse response h(n) and a frequency response HD(ω), which ideally satisfies the condition,

HD(ω)=1, |ω| ≤ π/D

=0, otherwise

Thus the filter eliminates the spectrum of X(ω) in the range π/D < ω < π.