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From: dk@speech..bellcore.com (Dan Kahn)
Subject: Re: Q : LPC - Spectrum
Message-ID: <CoKy8H.926@walter.bellcore.com>
Sender: news@walter.bellcore.com
Nntp-Posting-Host: speech.bellcore.com
Organization: Bellcore
References: <kordmann.766763181@ldv01> <2p2poa$bol@infa.central.susx.ac.uk> <2p3fpb$bd@dr-pepper.East.Sun.COM>
Date: Wed, 20 Apr 1994 22:53:05 GMT
Lines: 23

> > To compute the
> >vocal tract spectrum from the LPC coefficients, you could determine the
> >impulse response of the above mentioned IIR filter and then perform an
> >FFT on this response. 

The coeff's themselves are the impulse response of the FIR filter
which is the inverse of the desired IIR filter, so you can simply
take the FFT of the coeff's and invert the resulting spectrum.

> Just express the transfer function of the system in terms of the LPC coeffs.
> (constant-gain numerator, nth order polynomial denominator).
> Then evaluate the function on the unit circle (z=cos(a) +jsin(a)), varying
> angle a from 0 to pi.

Yes, this'll work (and allow you to calculate the spectrum just where
you want it).  Someone with access to an FFT-magnitude routine and an
aversion to complex numbers might prefer the approach above however...

> >Rod Dorrell (Bio-medical Engineering, University of Sussex, Brighton,
 
> Michael Scordilis

Dan Kahn, Bellcore
