A cepstrum is obtained by taking an inverse Fourier transform of a logarithm of a Fourier
transform. The real cepstrum of a function 
uses the logarithm
of the magnitude and is commonly defined by
![c(q)=F^(-1)[ln|F[x(t)]|](q).](/images/equations/Cepstrum/NumberedEquation1.svg) |
Some conventions instead use the logarithm of the power spectrum, which changes the result by a factor
of 2. The complex cepstrum instead uses a consistently chosen phase to define the
complex logarithm. The independent variable 
is called quefrency and has
units of time when 
does.
Taking a logarithm converts products in the spectrum into sums, so separated echoes or regularly spaced spectral peaks can produce distinct peaks in the cepstrum. Such periodic cepstral components are called rahmonics.
