# 0.2 Least mean squares adaptive filters

 Page 1 / 1

## Why lms?

In our system, the music that is being played by the computer is a known output that is being fed into the room, which has an unknown response, and picked up by the microphone. Since we have the signal both before and after the influence of the room, this is a candidate for an adaptive filter. The adaptive filter can be used to try to estimate the room’s response based on the music being outputted and the input to the microphone. Once an estimate is available, we can use it to remove the interference of the music from the input to the microphone.

## Lms overview

One of the most popular adaptive algorithms used today is the Least Mean Squares (LMS) algorithm. Essentially, this algorithm attempts to minimize the error that occurs between the detected (or desired signal), d[n], and the estimated value of the signal, y[n]. This estimated signal is created by taking the original input, x[n] , and running it through an approximation of the unknown channel. Basically:

$y\left[n\right]=x\left[n\right]\ast \stackrel{ˆ}{h}\left[0\right]+x\left[n-1\right]\ast \stackrel{ˆ}{h}\left[1\right]+\dots +x\left[n-N\right]\ast \stackrel{ˆ}{h}\left[N\right]$

or

$y\left[n\right]={x}_{N}^{T}\left[n\right]\ast \stackrel{ˆ}{h}\left[n\right]$

where N is the order to which you are approximating the unknown system, ${x}_{N}$ is a vector of the last N value of x, and each h[n] is a weight.

Once the signal and its approximation are found, the error is just the difference between the two signals at the current point in time.

$e\left[n\right]=d\left[n\right]-y\left[n\right]$

Using the error, we can approximate the next set of weights as follows:

$\stackrel{ˆ}{h}\left[n+1\right]=h\left[n\right]+\mu \ast e\left[n\right]\ast {x}_{N}\left[n\right]$

whereµis a constant.

## ChoosingΜ

The choice ofµis an important one as it greatly affects how the system will perform. Small values allow for greater precision in convergence, but slow down the response time of the system. If the value is too small, then the adaptive filter will not adapt fast enough. If it is too large, the system will not converge at all, and the value weights will actually diverge. Experimentation with different systems and environments is necessary to choose the ideal value forµ.

## Isolating the whistle

It can be shown that the error value will converge on a minimum point. This theoretical minimum will likely not be at zero error, since there is outside noise and interference, but it represents the original signal’s effect on d[n] being completely removed. In the case of our signal detection system, the whistle that we are trying to detect will still be in the e[n]and therefore we will use e[n] as the input to the rest of our system. Once the adaptive filter has settled down, this signal will be the input to the microphone minus the estimated value of the music when it reaches the microphone.

what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
how to synthesize TiO2 nanoparticles by chemical methods
Zubear
what's the program
Jordan
?
Jordan
what chemical
Jordan
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Got questions? Join the online conversation and get instant answers!