<< Chapter < Page
  Adaptive filters   Page 1 / 1
Chapter >> Page >

The weiner-filter, W opt R P , is ideal for many applications. But several issues must be addressed to use it in practice.

In practice one usually won't know exactly the statistics of x k and d k (i.e. R and P ) needed to compute the Weiner filter.

How do we surmount this problem?

Estimate the statistics r xx l 1 N k 0 N 1 x k x k + l r xd l 1 N k 0 N 1 d k x k - l then solve W opt R P

Got questions? Get instant answers now!

In many applications, the statistics of x k , d k vary slowly with time.

How does one develop an adaptive system which tracks these changes over time to keep the system nearoptimal at all times?

Use short-time windowed estiamtes of the correlation functions.

r xx l k 1 N m N 1 0 x k - m x k - m - l
r dx l k 1 N m N 1 0 x k - m - l d k - m and W opt k R k P k

Got questions? Get instant answers now!

How can r xx k l be computed efficiently?

Recursively! r xx k l r xx k - 1 l x k x k - l x k - N x k - N - l This is critically stable, so people usually do 1 r xx l k r xx k - 1 l x k x k - l

Got questions? Get instant answers now!

Tradeoffs

Larger N more accurate estimates of the correlation valuesbetter W opt . However, larger N leads to slower adaptation.

The success of adaptive systems depends on x , d being roughly stationary over at least N samples, N M . That is, all adaptive filtering algorithms require that the underlying system varies slowly withrespect to the sampling rate and the filter length (although they can tolerate occasional step discontinuities in theunderlying system).

Computational considerations

As presented here, an adaptive filter requires computing a matrix inverse at each sample. Actually, since the matrix R is Toeplitz, the linear system of equations can be sovled with O M 2 computations using Levinson's algorithm, where M is the filter length. However, in many applications this may be too expensive, especiallysince computing the filter output itself requires O M computations. There are two main approaches to resolving the computation problem

  • Take advantage of the fact that R k 1 is only slightly changed from R k to reduce the computation to O M ; these algorithms are called Fast Recursive Least Squareds algorithms; all methods proposed so farhave stability problems and are dangerous to use.
  • Find a different approach to solving the optimization problem that doesn't require explicit inversion of thecorrelation matrix.

Adaptive algorithms involving the correlation matrix are called Recursive least Squares (RLS) algorithms. Historically, they were developed after the LMSalgorithm, which is the slimplest and most widely used approach O M . O M 2 RLS algorithms are used in applications requiring very fast adaptation.

Questions & Answers

I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Adaptive filters. OpenStax CNX. May 12, 2005 Download for free at http://cnx.org/content/col10280/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Adaptive filters' conversation and receive update notifications?

Ask