ECE 673 - Random Signal Analysis I


Description

This is an introduction course to random analysis at graduate level which helps to build the theoretical foundation for students in communication, signal processing and networking areas. Topics include probability and random variables; random processes and sequences; linear system response to random input; special classes of random processes. Applications to signal detection and estimation are discussed throughout the course. 

Prerequisites

Linear system theory and random signal theory at undergraduate level.

Instructor

Dr. Osvaldo Simeone
Email: osvaldo.simeone@ njit.edu
Phone: (973) 596-5809
Office: 101 FMH Building 
Office Hour: Wednesday 4-6pm

Textbook

Intuitive probability and random process using MATLAB
Steven Kay
Springer, 2006.
(a partial electronic version can be downloaded here)

Requirements

There will two short tests (30% of grade), one midterm (30%), and one final exam (40%). Some of the problem sets will involve Matlab simulation. You can obtain a copy of Matlab software from the campus computing facility (here is a Matlab primer).

Weekly problem will be assigned and due the following class. The assignments will not be graded, but meant as an essential tool for the student to learn and for the teacher to assess the level of preparation of the class. (Cheating on assignments is then doubly inadvisable: it does not help the learning process and gives the teacher the wrong impression that the class is well prepared)


Spring 2006

 

Final grades (A: 9-10; B+: 8.5-9; B: 7.5-8.5; C+: 7-7.5; C: 6-7)

 

Midterm

 

Final v. A and final v. B

 


Fall 2007

 

Announcements:

 

- Sept. 27th class has been moved to Monday Sept. 25th in the same classroom (FMH 408) at the usual time (6-9pm).

 

- The first test will be on Oct. 4: one hour (6-7pm), open books and notes.

 

- The midterm will be on Oct. 25: three hours (6-9pm), one formula sheet allowed.

 

Links:

 

- a web page on the Monty Hall problem.

- a compendium on common probability mass functions and probability distribution functions

 

Suggested “light” reading

 

-          a book on how everything is connected (and the role of probabilistic models in investigating the problem)

-          a book on how order emerges from chaos (and the role of probabilistic models in investigating the problem)

 

Tests:

 

-          first test (Oct. 4) – solution and grades.

-          midterm (Oct. 25) – solution and grades.

-          second test (Nov. 29) - solution and grades.

-          final (Dec. 20) - solution and final grades.


Fall 2006: Tentative schedule

Week

Date

Plan

Chapter covered*

Homework

1

Sept. 6

Probability, conditional probability (1)

Ch. 1, 3, 4

HW01

Solution

(+ 1 extra problem)

2

Sept. 13

Probability, conditional probability (2)

Ch. 1, 3, 4

HW02

Solution 

3

Sept. 20

Discrete random variables

Ch. 5, 6

HW03

Solution 

4

Sept. 25

Continuous random variables

Ch. 10, 11

HW04

Solution

5

Oct. 4

Discrete multiple random variables

Ch. 7, 8, 9

HW05

Solution

6

Oct. 11

Continuous multiple random variables

Ch. 12, 13, 14

HW06

Solution

7

Oct. 18

Limit theorems

Ch. 15

 

8

Oct. 25

Midterm

  

 

9

   Nov. 1

Random processes, stationarity (1)

Ch. 16, 17

HW07

Solution

10

Nov. 8

Random processes, stationarity (2)

Ch. 16, 17

HW08

Solution

11

Nov. 15

Linear systems and stationary processes (1)

Ch. 18

HW09

Solution

12

Nov. 29

Linear systems and stationary processes (2)

Ch. 18

 

13

Dec. 6

Gaussian and Poisson processes

Ch. 20, 21

 

 

14

Dec. 13

Markov chains

Ch. 22

 

15

Dec. 20

Final

 

 

 *See class notes for sections covered.