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 ) = ∑ k = 0 N a k z − k The bandwidth-expanded filter can be expressed as:
A ′ ( z ) = ∑ k = 0 N a k γ k z − k In other words, each coefficient a k in the original filter is simply multiplied by γ 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.
