EE 503 : Lecture 21 (Fall 2020, METU)

EE 503 - Statistical Signal Processing and Modeling
Fall 2020, Middle East Technical University, Ankara, Turkey.
Instructor: Prof. Cagatay Candan
Lecture 21

Lecture Contents:
0:00 - Auto-correlation calculation, (LTI processing of WSS processes)
0:58 - Step 1: Cross-correlation calculation (auto-correlation calculation)
7:34 - Step 2: Auto-correlation calculation (auto-correlation calculation)
11:54 - Power spectral density
14:46 - Evaluation of output auto-correlation and input-output cross-correlation with Fourier transform
15:50 - DTFT of conj( h[ -n ] )
19:53 - Output power spectral density relations in Fourier-domain
22:30 - Z transform of conj( h[ -n ] )
27:00 - Output power spectral density relations in z-domain
30:28 - H(z) and H^*(1/z^*); conjugate reciprocal pole/zero pairs
40:57 - Power Spectral Density (properties)
41:00 - Property 1: Power spectral density is real valued
44:25 - Property 2: Power spectral density is non-negative (proved later)
44:48 - Property 3: Area under power spectral density is r_x[0] = E{ | x[n] |^2 }