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

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 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 Adaptive Digital Filters 3

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.” Adaptive Digital Filters 4

≡ Adaptive Digital Filters 5

Ali H. Sayed, Adaptive filters . John Wiley & Sons, 2011. Torsten Soderstrom, and Petre Stoica. System identification . Prentice hall, 2001. Adaptive Digital Filters 6

Channel Estimation Adaptive Digital Filters 7

Channel Equalization Adaptive Digital Filters 8

Communications • Adaptive -capacity -transmission rate -signal-to-noise ratio maximization for communication networks • Transmission noise cancellation • Acoustic/video noise cancellation • Synchronization • . . . Adaptive Digital Filters 9

Prediction * Stock market price signals * Weather forecast Adaptive Digital Filters 10

Control Adaptive Digital Filters 11

Networks * Adaptation and learning over networks, e.g. social media Adaptive Digital Filters 12

These were just a few out of many . . . Adaptive Digital Filters 13

• I. Introduction & Fundamentals - Basics of Estimation 1. Optimal estimation 2. Linear estimation -Basics of Optimization • II. Modeling & Filter Selection Adaptive Digital Filters 14

• 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 Adaptive Digital Filters 15