Bandwidth expansion explained

Bandwidth expansion is a technique for widening the bandwidth or the resonances in an LPC filter. This is done by moving all the poles towards the origin by a constant factor

\gamma

. The bandwidth-expanded filter

A'(z)

can be easily derived from the original filter

A(z)

by:

A'(z)=A(z/\gamma)

Let

A(z)

be expressed as:

A(z)=

	N
\sum
	k=0

	-k
a
	kz

The bandwidth-expanded filter can be expressed as:

A'(z)=

	N
\sum
	k=0

	kz
a
	k\gamma

^-k

a_k

in the original filter is simply multiplied by

\gamma^k

in the bandwidth-expanded filter. The simplicity of this transformation makes it attractive, especially in CELP coding of speech, where it is often used for the perceptual noise weighting and/or to stabilize the LPC analysis. However, when it comes to stabilizing the LPC analysis, lag windowing is often preferred to bandwidth expansion.

References

P. Kabal, "Ill-Conditioning and Bandwidth Expansion in Linear Prediction of Speech", Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, pp. I-824-I-827, 2003.