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Hilbert Transform Relations

Closely related to the cepstrum are the so-called Hilbert transform relations that relate the real and imaginary parts of the spectra of causal signals. In particular, for minimum-phase spectra, the cepstrum is causal, and this means that the log-magnitude and phase form a Hilbert-transform pair. Methods for designing allpass filters have been based on this relationship (see §B.2.2). For more about cepstra and Hilbert transform relations, see [60].


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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