Question

The mapping z^-1 → g(z^-1) must be __________

(a) Low pass

(b) High pass

(c) Band pass

(d) All-pass

The question was asked during an interview.

I want to ask this question from Frequency Transformations in the Digital Domain topic in portion Digital Filters Design of Digital Signal Processing

Answer 1

Right option is (d) All-pass

The explanation: We know that the unit circle must be mapped inside the unit circle.

Thus it implies that for r=1, e^-jω = g(e^-jω)=|g(ω)|.e^j arg [ g(ω) ]

It is clear that we must have |g(ω)|=1 for all ω. That is, the mapping is all-pass.