I was reading this text from Oppenheim and Schafer, briefly explaining the concept of the cepstrum. I'm new to this concept.

He explains that the cepstrum is useful to quantize the distance between 'echoes' of a signal. This echo value can be obtained analysing the first peak in the “spectrum” of the log spectrum from the original signal, since it will bring with itself the time delay through the Spectral density and log operations.

He also describes this peak as a 'rahmonic'.

My question: considering an audio source like a voice or an musical instrument, is the first rahmonic related to the first partial of a sound (a.k.a. the pitch of a sound)?

I'm asking this because it seems these 'echoes', related to the timbre of a sound, are not only periodic, but the lowest partial in the signal.

Also, if both values are related, why a cepstrum representation, like MFCC, is useful? Aren't Frequency-domain representations (like STFT, CQT, chromagram, etc.) enough?

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  • $\begingroup$ Is it possible to talk a little bit more about what the diagram represents? That "Frequency" is probably "Quefrency" (?). Quefrency is related to time....but not in that way (i.e. measuring it in "ms"). Quefrency is the frequency by which harmonics appear in the spectrum. Would it be possible to add the amplitude spectrum to the plots, as well as adapt the x-axis to depict Hz please? (On both the spectra plots). $\endgroup$ – A_A Aug 6 '20 at 10:20

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