Bandwidth expansion is a technique for widening the bandwidth or the resonances in an LPC

Linear predictive coding

Linear predictive coding is a tool used mostly in audio signal processing and speech processing for representing the spectral envelope of a digital signal of speech in compressed form, using the information of a linear predictive model...

 filter. This is done by moving all the poles towards the origin by a constant factor . The bandwidth-expanded filter can be easily derived from the original filter

Digital filter

In electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is...

  by:


Let be expressed as:


The bandwidth-expanded filter can be expressed as:


In other words, each coefficient

Linear prediction

Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples....

  in the original filter is simply multiplied by 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

Weighting filter

A weighting filter is used to emphasise or suppress some aspects of a phenomenon compared to others, for measurement or other purposes.- Audio applications :...

 and/or to stabilize the LPC analysis. However, when it comes to stabilizing the LPC analysis, lag windowing

Lag windowing

Lag windowing is a technique that consists of windowing the auto-correlation coefficients prior to estimating Linear prediction coefficients . The windowing in the auto-correlation domain has the same effect as a convolution in the power spectral domain and helps stabilizing the result of the...

is often preferred to bandwidth expansion.