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Least mean squares adaptive filters

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 [ n ] = x [ n ] h ˆ [ 0 ] + x [ n 1 ] h ˆ [ 1 ] + + x [ n N ] h ˆ [ N ] size 12{y \[ n \] =x \[ n \]* { hat {h}} \[ 0 \] +x \[ n - 1 \]* { hat {h}} \[ 1 \] + dotslow +x \[ n - N \]* { hat {h}} \[ N \] } {}


y [ n ] = x N T [ n ] h ˆ [ n ] size 12{y \[ n \] =x rSub { size 8{N} } rSup { size 8{T} } \[ n \]* { hat {h}} \[ n \] } {}

where N is the order to which you are approximating the unknown system, x N size 12{x rSub { size 8{N} } } {} is a vector of the last N value of x, and each h[n] is a weight.

Lms algorithm block diagram

x[n] is the input to the filter, v[n]is the interference in the room, h[n] is the impulse response we're modeling, and e[n]is the error in this modeling.

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 [ n ] = d [ n ] y [ n ] size 12{e \[ n \] =d \[ n \]- y \[ n \] } {}

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

h ˆ [ n + 1 ] = h [ n ] + μ e [ n ] x N [ n ] size 12{ { hat {h}} \[ n+1 \] =h \[ n \]+μ*e \[ n \] *x rSub { size 8{N} } \[ n \]} {}

whereµis a constant.


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.

Questions & Answers

what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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.
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I think
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Brian Reply
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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