User`s guide

LMS Adaptive Filter
5-268
5LMS Adaptive Filter
Purpose Compute filter estimates for an input using the LMS adaptive filter algorithm.
Library Filtering / Adaptive Filters
Description The LMS Adaptive Filter block implements an adaptive FIR filter using the
stochastic gradient algorithm known as the normalized Least Mean-Square
(LMS) algorithm.
The variables are as follows.
To overcome potential numerical instability in the tap-weight update, a small
positive constant (a = 1e-10) has been added in the denominator.
To turn off normalization, deselect the
Use normalization check box in the
parameter dialog box. The block then computes the filter-tap estimate as
The block icon has port labels corresponding to the inputs and outputs of the
LMS algorithm. Note that inputs to the
In and Err ports must be sample-based
Variable Description
n The current algorithm iteration
u(n) The buffered input samples at step n
The vector of filter-tap estimates at step n
y(n) The filtered output at step n
e(n) The estimation error at step n
d(n) The desired response at step n
µ The adaptation step size
yn() w
ˆ
H
n 1–()un()=
en() dn() yn()–=
w
ˆ
n() w
ˆ
n 1–()
un()
au
H
n()un()+
---------------------------------------
µe
∗
n()+=
w
ˆ
n()
w
ˆ
n() w
ˆ
n 1–()un()µe
∗
n()+=