Bandwidth expansion

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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 γ. The bandwidth-expanded filter A'(z) can be easily derived from the original filter A(z) by:

A'(z) = A(z / γ)

Let A(z) be expressed as:

A(z) = \sum_{k=0}^{N}a_kz^{-k}

The bandwidth-expanded filter can be expressed as:

A'(z) = \sum_{k=0}^{N}a_k\gamma^kz^{-k}

In order words, each coefficient ak in the original filter is simply multiplied by γk in the bandwidth-expanded. 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.

[edit] 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.

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