In this paper, a specific application of cepstral processing is consid
ered to illustrate homomorphic signal processing, In particular, an an
alytic expression is derived for the frequency domain representation o
f a signal that has been recovered from a multi-path signal with cepst
ral processing, The multi-path signal is composed of time-delayed, sca
led versions of the transmitted signal, and the transmitted signal is
to be recovered, The recovered signal is expressed analytically in the
frequency domain, By truncating an infinite series, the recovered sig
nal can be expressed in the time domain, The analytic expressions can
be used to predict the distortion that will result in the recovered si
gnal when the cepstral processing is implemented with Discrete Fourier
Transforms (DFTs), The analytic expression of a recovered signal is c
ompared with the signal recovered with DFTs, The signal recovery from
a multi-path signal that is composed of the transmitted signal and an
amplified version of the transmitted signal is discussed and considere
d in two examples, The examples also demonstrate the scaling of nomnin
imum phase signals to minimum phase signals.