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The mapping z^-1 → g(z^-1) must be __________(a) Low pass(b) High pass(c) Band pass(d) All-passThe 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»

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.



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