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Fall 2017 Mojtaba Soltanalian
Adaptive: real-time, online, cognitive
Filtering (of signals/systems from experimental data):
1. Mathematical modeling of the desired output
2. Identifying the best parameters for the model
3. Keeping up with the possible changes
Adaptive Digital Filters 2
1. Mathematical modeling of the desired output(i.e. determining the filter structure, and its free coefficients)
2. Identifying the best parameters for the model (or the filter coefficients)(usually by minimization of a function that penalizes the fitting error)
3. Keeping up with the possible changes
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Remarks:We have a FILTER- with coefficients varying in time according to certain rules (coefficient optimization).
This is key to smart/cognitive/adaptive systems:
- “systems with abilities to sense the environment,
learn, and interact with the environment.”
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5Adaptive Digital Filters
Ali H. Sayed,
Adaptive filters.
John Wiley & Sons, 2011.
Torsten Soderstrom, and Petre Stoica.
System identification.
Prentice hall, 2001.
6Adaptive Digital Filters
Channel Estimation
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Channel Equalization
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Communications
• Adaptive -capacity-transmission rate-signal-to-noise ratio
maximization for communication networks
• Transmission noise cancellation
• Acoustic/video noise cancellation
• Synchronization• . . .
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Prediction
* Stock market price signals
* Weather forecast
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Control
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Networks
* Adaptation and learning over networks, e.g. social media
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These were just a few out of many . . .
13Adaptive Digital Filters
• I. Introduction & Fundamentals-Basics of Estimation
1. Optimal estimation
2. Linear estimation
-Basics of Optimization
• II. Modeling & Filter Selection1. AR models 2. MA models
3. ARMA models 4. Arbitrary models
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• III. Filter Optimization & AdaptationSteepest–Descent Algorithms
Stochastic–Gradient Algorithms
Least Mean-Square (LMS) Algorithm
Recursive Least Squares (RLS) Algorithm
Kalman Filtering
• IV. Performance of Adaptive Filters
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