1. Instructor :Dr. Aamer Iqbal Bhatti
ADAPTIVE FILTERS I
Text Book: Adaptive Signal Processing
B. Widrow and S. D. Stearns, Prentice Hall, Englewood, 1985.
ISBN:
Reference Book : Adaptive Filter Theory (4th Edition) by Simon S. Haykin,
ISBN:
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2. Definition
Adapt, v.t., 1. To make suitable to requirements or conditions; adjust or modify fittingly (Random House Dictionary, 1971)
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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
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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
Submit your addresses (preferably at yahoo) to Salman
Labs will be arranged according to class strength
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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.
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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)
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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.
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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
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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
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10. Characteristics Automatic adaptation Specific filtering
Do not need to be designed
Self-healing
More complex
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11. Applications Overview
Modeling and system identification
Design and testing
Adaptive noise cancellation
Echo cancellation
Inverse modeling
Inverse filtering
Deconvolution
Equalization
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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
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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
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14. Monday, November 12, 2018Monday, November 12, 2018Monday, November 12, 2018
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15. Types of Adaptation Closed loop adaptation
Output signal is used for filter adjustment
Automatic adjustment
Responsive to changing conditions
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16. Monday, November 12, 2018Monday, November 12, 2018Monday, November 12, 2018
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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
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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
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19. Example
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20. Kinds of Estimation
Filtering: is an operation that incurs the extraction of information about a quantity of interest at time n
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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
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22. Kinds of Estimation Prediction: is the forecasting side of estimation
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23. Linear Optimum Filters
Statistical approach
Availability of the following information is assumed
Statistical characteristics of the noisy data
Statistical characteristics of useful signals
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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
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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
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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
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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
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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
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29. Applications
Identification: Adaptive filter is used to provide a linear model that represents the best fit to an unknown plant
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30. Applications
Inverse Modeling: provide an inverse model for the process generating noisy data
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31. Applications
Prediction: function of an adaptive filter to provide the best estimate of the future values of a signal
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32. Applications
Interference: Cancellation: adaptive filter is used to cancel unknown interference contained in a primary signal
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33. Task Read Chapter 1 of Widrow’s book
Read the “Introduction and Background” from the Haykin’s book (optional)
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