Lecture 42 Blog, ECE302 Spring 2013, Prof. Boutin
Monday April 22, 2013 (Week 16) - See Course Outline.
(Other blogs 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41
In the first part of Lecture 42, we continued characterizing the output of an LTI system when the input is a w.s.s. random process (i.e. w.s.s. random signal). We had previously seen a simple formula relating the mean of the output to the mean of the input (Fact 1). We then stated and proved that the response of the system to a w.s.s. random input is also w.s.s. (Fact 2). The third fact we covered relates the cross-correlation between the input and and the output random signals to the unit impulse of the system and the autocorrelation of the input. More specifically, the output is the convolution of the autocorrelation of the input with the unit impulse response of the system.
In the second part of Lecture 42, we introduced the concept of Power Spectral density of a w.s.s. random process. Two equivalent definitions were given, the first one of which (with the limit) was used to get an intuitive understanding of what the function represent (i.e. expected power for frequency f component of the random signal.)
Action items for students (to be completed before you attempt the practice final exam)
- Read Sections 10.1 (intro), 10.1.1 , 10.2 (intro), 10.2.1 in the textbook. NOTE THAT WE ARE NOT COVERING THE CASE OF DT RANDOM PROCESSES IN CHAPTER 9.
- Solve problems 10.1, 10.2, 10.6, 10.22 (make sure to know how to find the frequency response from the diff. ed.), 10.33a. NOTE THAT YOU CAN USE A TABLE OF CT FOURIER TRANSFORMS TO DO THESE PROBLEMS.
- Review everything to get ready for the final exam.
NOTE: 10.33a is being removed from the assigned problem list. You do not have to solve this problem.
Previous: Lecture 41
Next: Lecture 43
