## Conversion to Minimum Phase

As discussed in §11.7, any spectrum can be converted to
minimum-phase form (without affecting the spectral magnitude) by
computing its cepstrum and replacing any anticausal components with
corresponding causal components. In other words, the anticausal part
of the cepstrum, if any, is ``flipped'' about time zero so that it
adds to the causal part. Doing this corresponds to
*reflecting*
non-minimum phase zeros (and any unstable poles) inside the unit
circle in a manner that preserves spectral magnitude. The original
spectral phase is then replaced by the unique minimum phase
corresponding to the given spectral magnitude.

A matlab listing for computing a minimum-phase spectrum from the magnitude spectrum is given in §J.11.

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Hilbert Transform Relations

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Poles and Zeros of the Cepstrum