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Is it possible to implement an ideal allpass filter in Matlab? The filter response should be like this:

enter image description here

Note: the photo is imaginary (I did it using paint).

jojeck
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Amro Goneim
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    If the desired phase response is linear, then it depends on the slope of the phase if the filter can be realized exactly or only approximately. – Matt L. Jun 15 '21 at 10:30
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    This answer spells out how to do fractional delays and what the theory is behind it. It is simply based on the Nyquist-Shannon sampling and reconstruction theorem. – robert bristow-johnson Jun 15 '21 at 15:14

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Yes, of course. Any delay will look like this where the size of the delay determines the slope of the phase. If the the delay turns out to be an integer number of samples, than this very easy to implement. You can also do fractional delays but that's more work and can only be done approximately.

Hilmar
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    and if the delay, in units of samples, is fractional (or has a fractional component), there will be a minimum amount of delay that could be something like 8 or 16 or maybe more samples, just to decently represent the polyphase impulse response (what might usually be a windowed sinc function). – robert bristow-johnson Jun 15 '21 at 15:11