Thoughts On Adaptive Filtering Algorithms

Adaptive filtering algorithms have been used in wide areas including communication, signal processing,

control systems, biomedical, etc. A basic thought about adaptive filtering and its principles is needed for

the proper understanding of allied techniques. In the field of ANC, I have encountered manly Least

Mean Square (LMS) and Filtered-x LMS.

control systems, biomedical, etc. A basic thought about adaptive filtering and its principles is needed for

the proper understanding of allied techniques. In the field of ANC, I have encountered manly Least

Mean Square (LMS) and Filtered-x LMS.

Some thoughts around which these ideas can be framed as follows. Why should one go for adaptive

filtering? why don't normal filtering alone would fine?. How adaptive the so-called adaptive algorithm

would be? Is there a measure or metric for the adaptiveness property? What is the difference between

LMS and Recursive Least Squares (RLS) algorithm will be?. What are the assumptions around which

adaptive algorithms are framed upon?. Are they guaranteed to converge in all cases?

filtering? why don't normal filtering alone would fine?. How adaptive the so-called adaptive algorithm

would be? Is there a measure or metric for the adaptiveness property? What is the difference between

LMS and Recursive Least Squares (RLS) algorithm will be?. What are the assumptions around which

adaptive algorithms are framed upon?. Are they guaranteed to converge in all cases?

RLS Detour

The Wikipedia page of RLS says a few important points about its characteristics. The cost function is

the least squares. Does that mean it is not taking the mean value like in LMS?. One assumption for

RLS is that the input signal is considered to be deterministic. If that is the case then why would we

need to predict the signal at all? or Am I missing something big here?. In LMS the input signals are

considered to be stochastic. RLS offers fast convergence compared to its competitors at the cost of

computational complexity. One surprising thing I learned was that the inventor RLS is Gauss!.

Why and at what part computational complexity comes is to be explored.

the least squares. Does that mean it is not taking the mean value like in LMS?. One assumption for

RLS is that the input signal is considered to be deterministic. If that is the case then why would we

need to predict the signal at all? or Am I missing something big here?. In LMS the input signals are

considered to be stochastic. RLS offers fast convergence compared to its competitors at the cost of

computational complexity. One surprising thing I learned was that the inventor RLS is Gauss!.

Why and at what part computational complexity comes is to be explored.