THE REAL AND COMPLEX CEPSTRUM

The real cepstrum of a digital signal x(n) is defined as:
and the complex cepstrum is defined as:
where the complex logarithm is used:
Note that the real cepstrum, c(n), is the even part of complex cepstrum:
The word cepstrum was coined by reversing the first syllable in the word spectrum. The cepstrum exists in a domain referred to as quefrency (reversal of the first syllable in frequency) which has units of time.