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The filter with the system function H(z)=z^-k is a ____________

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The filter with the system function H(z)=z^-k is a ____________

(a) Notch filter

(b) Band pass filter

(c) All pass filter

(d) None of the mentioned

I have been asked this question during an interview.

I'd like to ask this question from LTI System as Frequency Selective Filters topic in portion Frequency Analysis of Signals and Systems of Digital Signal Processing

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The correct choice is (c) All pass filter

The explanation is: The system with the system function given as H(z)=z^-k is a pure delay system. It has a constant gain for all frequencies and hence called as All pass filter.

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