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

3Adaptive Digital Filters

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.”

4Adaptive Digital Filters

≡

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

7Adaptive Digital Filters

Channel Equalization

8Adaptive Digital Filters

Communications

• Adaptive -capacity-transmission rate-signal-to-noise ratio

maximization for communication networks

• Transmission noise cancellation

• Acoustic/video noise cancellation

• Synchronization• . . .

9Adaptive Digital Filters

Prediction

* Stock market price signals

* Weather forecast

10Adaptive Digital Filters

Control

11Adaptive Digital Filters

Networks

* Adaptation and learning over networks, e.g. social media

12Adaptive Digital Filters

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

14Adaptive Digital Filters

• 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

15Adaptive Digital Filters