You can use the estimated cepstrum to identify echoes or periodic components in a time series.

A cepstrum, which is an anagram of the word spectrum, is the Fourier transform of the natural logarithm of a spectrum. A cepstrum also is useful for separating homomorphic or convolved components in a time series by transforming the time series into a domain where the convolution becomes a simple summation operation.

Cepstrum estimation methods treat frequency-domain data as time-domain data. Therefore, the domain of a cepstrum is called quefrency, which is an anagram of the word frequency.

A cepstrum has the following four derivative forms: