Question

If HD(ω) is the frequency response of the low pass filter, then for what value of ω, HD(ω)=1?

(a) |ω| = π/D

(b) |ω| ≥ π/D

(c) |ω| ≤ π/D

(d) None of the mentioned

The question was asked in an international level competition.

I want to ask this question from Decimation by a Factor D in chapter Multirate Digital Signal Procesing of Digital Signal Processing

Answer 1

Right option is (c) |ω| ≤ π/D

The explanation is: 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.