DSP Lecture 20: The Wiener filter

ECSE-4530 Digital Signal Processing
Rich Radke, Rensselaer Polytechnic Institute
Lecture 20: The Wiener filter (11/10/14)

0:00:03 Review of autoregressive (AR) processes and parameter estimation
0:06:06 Optimal linear discrete-time filters (Wiener filters)
0:10:03 Problem setup and cost function
0:12:37 Taking the derivative of the cost function
0:16:41 The orthogonality property
0:19:38 The Wiener-Hopf equations
0:22:27 The Wiener-Hopf linear system for an FIR filter
0:26:21 Computing the error for the optimal filter
0:30:05 The result
0:31:45 Proof that the Wiener filter is optimal and unique
0:34:38 Linear prediction
0:38:19 One-step-ahead linear prediction equations
0:44:17 Error for one-step-ahead predictor
0:45:55 The augmented system for the optimal predictor and error
0:49:22 Goal: find an optimal longer filter from a shorter one
0:53:12 Backward prediction
0:55:37 The relationship between forward and backward prediction
0:59:22 The Levinson-Durbin algorithm
1:01:15 Reflection coefficients
1:02:36 Deriving the Levinson-Durbin equations
1:11:15 The final result

Follows Section 12.7 of the textbook (Proakis and Manolakis, 4th ed.).