Taylor – Section 12.3 – The cepstrum

The diagram in Taylor is correct.

You can work this out yourself from first principles: taking the log will compress the vertical range of the spectrum, bringing the very low amplitude components up so we can see them, and bringing the high amplitudes (the harmonics, in this case) down.

J&M messed up when they quoted it – a lesson in not quoting something unless you really understand it, perhaps!? Or maybe a printer’s error.

Taylor is separating it out here because he is trying to show how the equations align with the physics of sound propagation in the vocal tract.

Lip radiation can be assumed a constant effect: effectively, a filter that boosts high frequencies. This filtering effect is independent of the configuration of the articulators (Taylor, 2009, equation 11.29).

Furthermore, the constant high-pass filtering effect of lip radiation is more than cancelled out by another constant effect of low-pass filtering at the sound source:

It is this, combined with the radiation effect, that gives all speech spectra their characteristic spectral slope.

(Taylor, 2009, page 332)

So, we don’t need any learnable model parameters for these effects. We can account for them either by absorbing this constant effect into the vocal tract filter (which might be modelled using linear prediction) or by pre-emphasising the signal in the time domain (Taylor, 2009, page 375) to make its spectrum flatter, before any subsequent modelling, processing or feature extraction.

Pre-emphasis is standard practice in most speech processing – can you find where this is done in the digit recogniser ?