The cepstrum is defined as the inverse [[discrete Fourier transform (DFT)]] of the log magnitude of the DFT of a signal. $ c(n) = \cal{DFT}^{-1}\{\ln(\cal{DFT}\{x(n)\})\} $ That is $ c(n) = \sum_{n=0}^{N-1} \ln\left(\left|\sum_{n=0}^{N-1} x(n) e^{-j 2\pi kn/N}\right|\right)e^{j 2\pi kn/N} $ In a block diagram: ![[cepstrum.excalidraw.svg]] The cepstrum of the signal separates the spectral envelope from the harmonic spectrum. The first is slowly varying corresponding to lower indexes of $c(n)$ and the latter is more rapidly changing and corresponds to higher indexes of $c(n)$.