2.9 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Bandwidth expansion | 1/1 | https://en.wikipedia.org/wiki/Bandwidth_expansion | reference | science, encyclopedia | 2026-05-05T12:04:12.339066+00:00 | kb-cron |
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
{\displaystyle \gamma }
. The bandwidth-expanded filter
A
′
(
z
)
{\displaystyle A'(z)}
can be easily derived from the original filter
A
(
z
)
{\displaystyle A(z)}
by:
A
′
(
z
)
=
A
(
z
/
γ
)
{\displaystyle A'(z)=A(z/\gamma )}
Let
A
(
z
)
{\displaystyle A(z)}
be expressed as:
A
(
z
)
=
∑
k
=
0
N
a
k
z
−
k
{\displaystyle A(z)=\sum _{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
{\displaystyle A'(z)=\sum _{k=0}^{N}a_{k}\gamma ^{k}z^{-k}}
In other words, each coefficient
a
k
{\displaystyle a_{k}}
in the original filter is simply multiplied by
γ
k
{\displaystyle \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.