a simple question on adaptive filtering

[scholar_a]

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

 

[fontp]

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]

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]

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

The Wiener filtering usually executes an optimal tradeoff between inverse filtering and noise smoothing.
https://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" ))
https://en.wikipedia.org/wiki/Similarities_between_Wiener_and_LMS

 

[scholar_a]

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]

Exactly. FIR filter built by block algorithm

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

 

[khubaibahmed]

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)

 

[s.san2006]

you can refer to adaptive filtering techniques by Simon Haykins. Trust me, it's a good book.