a simple question on adaptive filtering

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scholar_a

Joined: 04 Jul 2007
Posts: 127
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12 Jun 2008 6:49 a simple question on adaptive filtering

What is the difference between "Wiener filtering" and "LMS algorithm" ?

fontp

Joined: 19 Nov 2004
Posts: 129
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13 Jun 2008 14:48 a simple question on adaptive filtering

Wiener filtering is an optimal filtering against noise, when stohastic properties of signal and noise are provided

LMS is linear channel identification algorithm. For given determenistic input and output signal we can determine impulse response of linear transform

No similarity (except mean squared error criteria used)

bhq

Joined: 11 Jun 2008
Posts: 81
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14 Jun 2008 12:34 Re: a simple question on adaptive filtering

Weiner and LMS both are adaptive filters and doing same thing. Both are stochastic based.
In weiner we need R Matrix (Correlation of input) and P Matrix (Cross Correlation of Input and output) and W=Inv(R) * P

So in wiener filter we need only R and P Matrix.

But In LMS are are minimising the MSE (Mean Square Error) It involves iteration. LMS is normaly used for adaptive filter.
Because in Wiener we need to compute inverse, it is not easy in hardware to implement. so we implement LMS

fontp

Joined: 19 Nov 2004
Posts: 129
Helped: 20

16 Jun 2008 9:21 a simple question on adaptive filtering

Well I was wrong in that "no similarity at all".

The Wiener filtering usually executes an optimal tradeoff between inverse filtering and noise smoothing.
http://www.owlnet.rice.edu/~elec539/Projects99/BACH/proj2/wiener.html
This problem, strictly speaking, has nothing in common with LMS, as it is used for restoration of original (input) signal, not estimation of transfer function

But as for system identification problem -yes, LMS is adaptive and approximate solution of Wiener-Hopf equations, that sometimes also is called 'Wiener filter for system identification" ))
http://en.wikipedia.org/wiki/Similarities_between_Wiener_and_LMS

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scholar_a

Joined: 04 Jul 2007
Posts: 127
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16 Jun 2008 18:14 Re: a simple question on adaptive filtering

so Wiener isn't iterative? once we have R and P matrixes and from these find the optimum W. here there is no errors, am I right?

Regards

fontp

Joined: 19 Nov 2004
Posts: 129
Helped: 20

16 Jun 2008 18:47 a simple question on adaptive filtering

Exactly. FIR filter built by block algorithm

LMS is adaptive iterative adaptive solution and so is RLS for inverse
http://en.wikipedia.org/wiki/Recursive_least_squares

khubaibahmed

Joined: 24 Aug 2005
Posts: 31
Helped: 2

17 Jun 2008 11:37 Re: a simple question on adaptive filtering

Weiner and LMS both are stochastic based filters. If we do not consider E[.] operator in Wiener then we will get an iterative form LMS of Wiener. So we can do same thing just by implementing an iterative Algo rather than implementing wiener filter which requires computation of inv(R)