ADAPTIVE FILTERS I

1. ADAPTIVE FILTERS I Text Book: AdaptiveSignalProcessing B. Widrow and S. D. Stearns, Prentice Hall, Englewood, 1985. ISBN: 0130040290 Reference Book : Adaptive Filter Theory (4th Edition)by Simon S. Haykin, ISBN:0130901261 Lecture 1 Instructor :Dr. Aamer Iqbal Bhatti

2. Definition Adapt, v.t., 1. To make suitable to requirements or conditions; adjust or modify fittingly (Random House Dictionary, 1971) Lecture 1

3. Course Contents Basic adaptive filters Optimization Concepts Least mean square filters Other adaptive algorithms Application to Real World Problems Stochastic processes and Models Prediction theory and Linear Prediction Lecture 1

4. Course Material Lecture PDFs One assignment per two week Lab exercises in MATLAB and SIMULINK Files will be available at yahoo group Address of the group is adaptivefilters@groups.yahoo.com Submit your email addresses (preferably at yahoo) to Salman Labs will be arranged according to class strength Lecture 1

5. Concept An adaptive entity is a system whose structure is alterable or adjustable in such a way that its behaviour or performance improves through contact with its environment, according to some desired criterion. Lecture 1

6. Everyday Example The input signal intensity to a radio receiver varies a lot. Need to keep the input power level with in certain range. Requires an online tuning of signal level A variable gain is the solution This is the concept of Automatic Gain Control (AGC) Lecture 1

7. AGC AGC is a multiplier whose gain is inversely proportional to the signal level. Thus trying to maintain the input power range. AGC acts as an adaptive gain to the receiver system. Lecture 1

8. Purpose of this course Introduce and motivate adaptive filters Derive the underlying laws and equations Explore probable areas of applications Implementation of adaptive filters in such applications Lecture 1

9. Adaptive Filters ??? Resembles with ordinary FIR filters However taps/coefficients/parameters of the filters are NOT designed These taps are adjusted online to meet certain criterion The change in taps is done through clever adaptation algorithms Lecture 1

10. Characteristics Automatic adaptation Specific filtering Do not need to be designed Self-healing More complex Lecture 1

11. Applications Overview • Modeling and system identification • Design and testing • Adaptive noise cancellation • Echo cancellation • Inverse modeling • Inverse filtering • Deconvolution • Equalization Lecture 1

12. Properties • Time-varying • Nonlinear • Principle of superposition does not hold • Fixed filters • Insufficient system information • Time varying systems/channels • Optimal for a certain class of systems/channels Lecture 1

13. Types of Adaptation • Open loop adaptation • Only input/system signal knowledge is used • Relatively straightforward • Supervisory kind of control • System specific knowledge is required • Cannot cope with time drifts Lecture 1

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15. Types of Adaptation • Closed loop adaptation • Output signal is used for filter adjustment • Automatic adjustment • Responsive to changing conditions Lecture 1

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17. Terminology Estimator or a filter is a system that is designed to extract information about a prescribed quantity of interest from noisy data There must be some criteria to distinguish between the useful signal and the noisy data Filters in frequency domain like low pass high pass etc. use frequency as the basis to distinguish between the two Lecture 1

18. Example Transmitted signal in a communication system is distorted by the Inter-Symbol Interference due to non ideal behavior of the channel Noise from the environment Job of the receiver is to estimate the transmitted signal Lecture 1

19. Example Lecture 1

20. Kinds of Estimation Filtering: is an operation that incurs the extraction of information about a quantity of interest at time n Lecture 1

21. Kinds of Estimation Smoothing: is a posteriori form of estimation . In that data measured after the time of interest are used in the estimation Lecture 1

22. Kinds of Estimation Prediction: is the forecasting side of estimation Lecture 1

23. Linear Optimum Filters Statistical approach Availability of the following information is assumed Statistical characteristics of the noisy data Statistical characteristics of useful signals Lecture 1

24. Linear Adaptive Filters For Stationary input we mean: Input is generated by the process whose statistical characteristics are not changing with time For stationary inputs the resulting solution is commonly known as Wiener Filter For non stationary environment Kalman Filter is the suitable solution Lecture 1

25. wiener Filter and Motive for Adaptive Filter Design of a wiener filter requires a prior information about the statistics of the data to be processed. wiener filter is optimum if the exact parameters are known If the parameters are changing with time or the exact values are not known than wiener solution is not optimum Lecture 1

26. Wiener Filter and Motive for Adaptive Filter An adaptive filter solves the problem by ‘estimate and plug ‘ approach This solution is costly in terms of computational resources it requires To mitigate this problem we use Adaptive Filters Lecture 1

27. Performance Evaluation of the Adaptive Filter Performance of an Adaptive Filter algorithm is analyzed based on following criteria Rate of convergence Miss adjustment Tracking Robustness Computational requirements Structure Lecture 1

28. Challenges for Adaptive Filter Designer Understand the capabilities and limitations of various adaptive filters Understanding the selection of the appropriate algorithm for the application at hand Lecture 1

29. Applications Identification: Adaptive filter is used to provide a linear model that represents the best fit to an unknown plant Lecture 1

30. Applications Inverse Modeling: provide an inverse model for the process generating noisy data Lecture 1

31. Applications Prediction: function of an adaptive filter to provide the best estimate of the future values of a signal Lecture 1

32. Applications Interference: Cancellation: adaptive filter is used to cancel unknown interference contained in a primary signal Lecture 1

33. Task Read Chapter 1 of Widrow’s book Read the “Introduction and Background” from the Haykin’s book (optional) Lecture 1