EE 503 : Lecture 12b (Fall 2020, METU)

EE 503 - Statistical Signal Processing and Modeling
Fall 2020, Middle East Technical University, Ankara, Turkey.
Instructor: Prof. Cagatay Candan
Lecture 12b

Playlist :    • EE503@METU, Fall 2020  

Lecture Contents:
00:00 - Random vectors
03:04 - Correlation matrix (definition)
03:31 - Covariance matrix (definition)
11:10 - Properties of covariance matrix
12:14 - Hermitian symmetry (properties continue)
15:18 - Positive semi-definiteness (properties continue)
20:47 - Gaussian Distribution
21:16 - 1D Gaussian r.v.
28:10 - N-dimensional Gaussian vectors
33:08 - 2-dimensional Gaussian vectors
40:15 - Level curves (2D Gaussian vectors)
45:15 - Level curves (2D Gaussian vector, Cx : diagonal)
49:10 - Level curves (2D Gaussian vector, Cx \propto I )
50:30 - Facts on Gaussian vectors
50:45 - Marginalization (facts continue)
52:48 - Example on marginalization of Gaussian vectors
55:30 - Linear processing of Gaussian vectors (facts continue)
56:15 - Example: Ry matrix in terms of Rx for y = Mx
1:02:13 - Example: Var ( \sum_{i=1}^N x_i ) (redo earlier example with vector operations)




Correction:
36:20 - 2D Gaussian case: pdf (2nd line on the left side) should have Cx^{-1} not Cx (Cagatay C.)