# Why does the excitation signal appear, separated, at high quefrencies in the cepstrum?

So, I've just begun a speech and language processing course and have found the explanation of the process of getting the cepstrum of a signal and its properties a little confusing. The following is a description of my current understanding and an explanation of confusion it's causing me:

1. start with the speech signal. we can think of it as the formant signal convolved with a the excitation signal which is a dirac comb (approximately).
2. take the FFT, giving the spectrum of the excitations multiplied with the spectrum of the formants. the FFT of the excitation signal is another dirac comb with period 1/T
3. take logs. so the 2 signals above are now added
4. inverse fourier transform - the two signals from 1 should now be combined in addition (the FT transform is linear)

So if those 4 step are right, then why does the excitation appear at a particular region in the quefrency domain? it should emerge as a Dirac comb, added to the formant impulse response shouldn't it?

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When using an FFT, an evenly spaced sequence of events in one domain usually produces a strong component in the other domain at a location related to the spacing of the events in the first domain.

A voiced speech signal usually includes a lot of harmonics which are evenly spaced in the frequency domain. These evenly spaced events in the frequency domain will thus produce a component in the quefrency domain whose location is related to the spacing of the harmonics. And the spacing of the harmonics in the frequency domain is related to the spacing of the exciter events in the time domain (the period of the fundamental).

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hi, thank-you for your answer, sorry for my slow response. I'm a little confused by your first statement. Do you think you could elaborate or give some examples? –  Sam Feb 17 '13 at 18:42