Fall 2019 Mojtaba Soltanalian Adaptive: real-time, online, - - PowerPoint PPT Presentation

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Jan 24, 2024 690 likes •850 views

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

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Fall 2019 Mojtaba Soltanalian

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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

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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 3 Adaptive Digital Filters

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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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≡

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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 & Adaptation

Steepest–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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