DSP Lecture 19: Introduction to adaptive filtering; ARMA processes

ECSE-4530 Digital Signal Processing
Rich Radke, Rensselaer Polytechnic Institute
Lecture 19: Introduction to adaptive filtering; moving average, autoregressive, and ARMA processes (11/6/14)

0:00:02 Introduction to adaptive filtering
0:03:44 Review of concepts from probability for stochastic signals
0:04:05 The CDF and PDF of a random variable
0:05:20 The mean
0:05:46 The autocovariance and autocorrelation
0:07:42 Stationary processes
0:10:02 Wide-sense-stationary processes
0:11:26 The correlation matrix
0:14:33 Models for stochastic signals
0:15:44 White Gaussian noise
0:17:13 Moving average (MA) model
0:19:16 Autoregressive (AR) model
0:21:19 The ARMA model
0:23:16 Estimating the parameters of an AR process
0:24:22 The Yule-Walker equations
0:27:16 Forming the corresponding linear system for the a's
0:30:52 The final result
0:32:15 Estimating the autocorrelations r from data
0:33:16 Estimating the variance sigma
0:35:30 The final equation
0:36:28 Estimating the model order M
0:39:41 Matlab example of AR parameter estimation

Follows Sections 12.1-12.2 of the textbook (Proakis and Manolakis, 4th ed.).