ADAPTIVE FILTERS

ADAPTIVE FILTERSPresented To:- Presented BY:-Ms. Priyanka Mishra Ankit Sharma Asstt. Professor BU2015PGEC001Electronics and communication Electronics and communicationEngineering Engineering IntroductionDefining an Adapter FilterBlock Diagram Of Adapter Filtering ProblemAdapter Filter StructureGradient Based Adaptive Filtering AlgorithmsThe Mean square Error cost functionThe Wiener Solution

ContentsIn many Practical scenario it is observed that we are required to filter a signal whose exact frequency response is not known.A solution to such problem is an adaptive filter.An adaptive filter is one which can automatically design itself and can detect system variation in time.IntroductionAn Adaptive filter is defined by four aspects:

The signal being processed by the filter.The structure that defines how the output signal of the filter is computed from its input signal.The parameters within this structure that can be iteratively changed to alter the filters input-output relationship.The adaptive algorithm that describes how the parameters are adjusted from one time instant to the next.

Defining an Adaptive Filter4

Block Diagram of adaptive Filtering ProblemThe error signal e(n) is calculated from the desired response as shown in block diagram.The error signal is fed into a procedure which alters or adapt the parameters of the filter from time n to time(n+1) in a well-defined manner.Thus as time increases the output signal or actual responses y(n) is hoped to become better and better match to the desired response d (n).Adaptive Filtering Problem

Adaptive Filter StructureSo far we are focusing on the desired response d(n). However, it is quite obvious that in many practical situation d(n) is not available.To solve this problem d(n) must be estimated from whatever signal is available to the input.The fact that such schemes even work is a tribute both to the ingenuity of the developers of the algorithms and to the technology maturity of the adaptive filtering field.Practical adaptive filtering Problem 1It should also be recognised that the relationship between x(n) and d(n) can vary with time.In this situation the adaptive filter must continuously change its parameter values to adapt the change.This behavior is commonly referred to as tracking.Practical adaptive filtering Problem 2The general form of an adaptive FIR filtering algorithm is W(n+1)=W(n)+(n)G(e(n),X(n),(n)) where, G(.)= particular vector valued non-linear function. (n)=Step size parameter (n)=Vector of statesGradient- Based Adaptive Filtering Algorithms

The Mean-Squared Error Cost FunctionThe MSE Adaptive filters is useful for adaptive FIR Filter because: has a well-defined minimum with respect to the parameters in W(n).The parameters at this minimum minimizes the power of the signal e(n), indicating that y(n) has approached d(n). is a smooth function of each parameter of W(n),and differentiable w.r.t. each of these parameters.The MSE cost Function (contd.)

The Wiener SolutionThis procedure adjusts each parameter of the system according to

For FIR Adaptive Filter This Relation Reduces to: The Method of Steepest Descent

Other ImplementationThere are various other methods also for implementation of Adapter Filter.The hardware or software implementation supporting floating point arithmetic are less sever compared to those supporting fixed point arithmetic.The LMS Algorithm is well known for its robust performance in the presence of finite precision error.Therefore LMS algorithm can be easily implemented in dedicated hardware using the general form of implementation given by-Discussion

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