## EEC260 – Random Signals And Noise

4 units – Winter Quarter

Lecture: 3 hours

Discussion: 1 hour

Prerequisite: STA 120, EEC 150A; EEC 250 recommended

Grading: Letter;  one take-home midterm exam and one take-home final exam.

Catalog Description:

Random processes as probabilistic models for signals and noise. Review of probability, random variables, and expectation. Study of correlation function and spectral density, ergodicity and duality between time averages and expected values, filters and dynamical systems. Applications.

Expanded Course Description:

1. Probability Random Variables, and Expectation (3 weeks)
1. The Notion of Probability
2. Sets
3. Sample Space
4. Probability Space
5. Conditional Probability
6. Independent Events
7. Random Variables
8. Probability Density
9. Functions of Random Variables
10. Expected Value
11. Moments and Correlation
12. Conditional Expectation
2. Introduction To Random Processes (1/2 week)
1. Introduction
2. Generalized Harmonic Analysis
3. Signal-Processing Applications
4. Types of Random Processes
3. Mean and Autocorrelation (1 week)
1. Definitions
2. Examples of Random Processes and Autocorrelations
4. Classes of Random Processes (1/2 week)
1. Specification of Random Processes
2. Gaussian Processes
3. Markov Processes
4. Stationary Processes
5. The Wiener and Poisson Processes (1 week)
1. Derivation of the Wiener Process
2. The Derivative of the Wiener Process
3. Derivation of the Poisson Process
4. The Derivative of the Poisson Counting Process
6. Ergodicity and Duality (1/2 week)
1. The Notion of Ergodicity
2. Mean-Square Ergodicity
3. Duality and the Role of Ergodicity
7. Linear Transformations, Filters, and Dynamical Systems (1 1/2 weeks)
1. Linear Transformation of an N-tuple of Random Variables
2. Linear Discrete-Time Filtering
3. Linear Continuous-Time Filtering
4. Dynamical Systems
8. Spectral Density (1 1/2 weeks)
1. Input-Output Relations
2. Expected Spectral Density
3. Coherence and Wiener Filtering
4. Time-Average Power Spectral Density and Duality
5. White Noise
6. Bandwidths
7. Spectral Lines
9. Autoregressive Models and Linear Prediction (1/2 week)