# Intuition behind cepstrum analysis terminology

In multiple books I found a parallel between spectrum-analysis terminology and cepstrum-analysis terminology that says

low pass filter $\rightarrow$ short pass lifter

I didn't read explicitly what lifter does, but assuming a short pass lifter passes short rahmonics just as low pass filter passes low harmonics, why the parallel isn't rather

low pass filter $\rightarrow$ long pass lifter

since low harmonics correspond to long rahmonics?

in filtering we try to separate two signals from each other. if two signals are added together this is the normal filtering. but these two signals could be multiplied or convoluted with each other. considering there are huge scientific background on this kind of filtering ( for additive signals) we try to transform other problems to this kind.

if signals multiplied with each other, we take the logarithm of their multiplication to convert it two additive signal. then we use filtering methods for additive signals.

if they were convoluted with each other, we know their spectrum is multiplied, so by taking the logarithm of their spectrum, we reach two additive spectrum in frequency domain. now we treat these two additive spectrum in frequency domain as two additive signals and apply the filtering methods for additive signals. considering we work on frequency domain signals if we use normal filtering terminology there would be some confusion e.g. if we say we use a low-pass filter someone might think we apply a LPF on our original time domain signal instead of their frequency domain counter part, so in order to avoid these confusions some new terminology is used.

now if we take Fourier transform of these frequency domain signals we go to time domain, so a low-pass filter (for frequency domain signals) becomes a short-pass filter which passes the signal at times before a cut-off time and high-pass filter becomes long-pass filter which passes the signals after a cut-off time.