1051-713 NOISE AND RANDOM PROCESSES

I. Course: 051-713 Noise and Random Processes

1.1 Four (4) credit hours

1.2 Four (4) lecture hours per week

1.3 Prerequisites: M.S. Imaging Science Core, An Introduction to Probability or Consent of Instructor

II. Course Catalog Description:

The purpose of this course is to develop an understanding and ability in modeling noise and random processes within the context of imaging systems. The focus will be on stationary random processes in both one dimension (time) and two dimensions (spatial). Power spectrum estimation will be developed and applied to signal characterization in the frequency domain. The effect of linear filtering will be modeled and applied to signal detection and maximization of SNR. The matched filter and the Wiener filter will be developed. Signal detection and amplification will be modeled, using noise figure and SNR as measures of system quality. At completion of the course, the student should have the ability to model signals and noise within imaging systems.

III. Course Objective:

3.1 Ability to model signals and noise within imaging systems

3.2 Modeling and analyzing problems using computer visualization

3.3 Familiarity. with modeling tools such as IDL, Matlab, Mathematica, or Mathcad

IV. Course Outline:

4.1 What is a random process? Develop the concept starting with the Poisson process to show the effect of combining a large number of discrete random events. This is a good concept for a lot of different situations, from quantum noise to shot noise. Achieve a normal r.p. as a limit. Examples: shot noise, quantum noise.

4.2 Moments of a random process. Focus particularly on second order moments, leading to a measure of power and the concept of correlation. Define a wide-sense stationary r.p. Develop autocorrelation in both 1-D and 2-D.

4.3 Power spectrum of a wss r.p. Relation to the autocorrelation function. Estimation of the powet spectrum. Illustrate with the estimation of the sunspot cycle from real data. Show how one can get into trouble with the periodogram. Show calculation in 1-D and 2-D.

1. Filtering of r.p. How to model the effect of a linear filter on a r.p. Begin with the continuous time model and then go over to sampled data model. Expand to 2-D filtering. Apply to rnatched filtering and signal detection. Define SNR and show how to design a Wiener filter.
2. Detection and amplification of signals. in noise. Address the problem of detector and amplifier noise added to the noise that comes in with the signal. Develop the idea 9f noise figure for cascaded systems and show good. system design practice to maximize SNR. Example: CCD. detection of faint signals. Radar detection of faint signals.

V. Instructional Techniques:

5.1 Lectures

5.2 Modeling

VI. Evaluation:

6.1 Exams

6.2 Programming Assignments

VII. Bibliography

7.1 . Marple, S. Laurence Jr. Digital Spectral Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ.