Fall 2019 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

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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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Ali H. Sayed,

Adaptive filters.

John Wiley & Sons, 2011.

Torsten Soderstrom, and Petre Stoica.

System identification.

Prentice hall, 2001.

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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 . . .

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• I. Introduction & Fundamentals-Basics of Estimation

1. Optimal estimation

2. Linear estimation

-Basics of Optimization

• II. Modeling & Filter Selection

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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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