# What is the difference between cepstral and temporal domains?

Some parameters of speech analysis occur in the temporal domain (those are the ones I typically understand: f0, formants, etc.) - but others occur in the so-called cepstral domain. If I google "cepstral domain" or "cepstrum", I see mostly mathematical stuff. Not what I'd call intelligible. Perhaps one of you has some a handy heuristic to understand how the cepstral domain differs from the temporal one from a speech perspective.

Thanks.

I was interested too so I looked up this lecture.

The definition it provides in the second slide is illuminating:

The cepstrum is defined as the inverse DFT of the log magnitude of the DFT of a signal

Okay, so it seems that the steps to get the cepstrum are:

1. Perform a Discreet Fourier Transform (DFT) on your time domain signal.
2. Take the logarithm of the magnitude of the spectrum that you get. (Because humans, in most cases, don't hear differences in the phase of an audio signal)
3. Perform the inverse DFT of the signal getting you back to a time domain signal but one that has been modified.

So, you probably know that you take the logarithm because humans hear on a logarithmic scale (that's why we use decibels). And performing the inverse DFT on the logarithm will go back from the frequency domain to the time domain. So, on the face of it, we are essentially trying to get a signal that looks more like our ears would actually hear it as opposed to how it actually looks according to the sensors.

In essence we are turning the input signal into a cepstrum signal that is easier for us to perform ear-like processing on.

I recommend reading that paper further to understand it better. And if somebody understands this better than I do then please chime in. You are basically reading my 5 min analysis.

• Brilliant. Very clear! Weird question but: Is there some acoustic object that can be measured both in the cepstral and spectral/temporal domains? Contrasting how the two domains changes the nature of the measurement would yield still more insight... this is a challenge to get my head around. Apr 1, 2015 at 8:47
• Yeah, I'm still not sure I've gotten this quite right. I'm still trying to work out what the exact advantages are that step 3 gives you. Apr 1, 2015 at 22:31