Re: Cepstrum computation (Paul Boersma )

Subject: Re: Cepstrum computation
From:    Paul Boersma  <boersma(at)FON.HUM.UVA.NL>
Date:    Wed, 23 Jun 1999 03:15:01 +0200

Laszlo Toth wrote:

> if(||FFT(x)||==0) { y=-BigNumber}
> else {y=log(||FFT(x)||)
>
> Where "BigNumber" is some big constant.

This is not correct, since you would like to preserve monotonicity, i.e. the relation that
smaller ||FFT(x)|| means smaller y (or at least not larger y). So it would have to be:

if (||FFT(x)|| <= exp(-BigNumber)) { y=-BigNumber}
else {y=log(||FFT(x)||)

But note that adding a small number makes the function differentiable:

    y = log (||FFT(x)|| + epsilon)

Bill Hartmann wrote:

> You can always add a little broadband noise to keep the power spectrum
> finite at all frequencies.

The "epsilon" trick is equivalent to adding white noise.
Perhaps we should instead add a noise whose spectrum is equivalent to
the zero-phon curve?

Paul Boersma
Institute of Phonetic Sciences, University of Amsterdam
Herengracht 338, 1016CG Amsterdam, The Netherlands
http://www.fon.hum.uva.nl/paul/