
25181: Random Process
Course Name: Random Process
Course Number: 25181
Prerequisite(s): 25111 (Communication Systems 1)
Co-requisite(s): 25162 (Spectrum Estimation)
Units: 3
Level: Postgraduate
Last Revision: Fall 2012
Description:
Syllabus:
References:
Course Number: 25181
Prerequisite(s): 25111 (Communication Systems 1)
Co-requisite(s): 25162 (Spectrum Estimation)
Units: 3
Level: Postgraduate
Last Revision: Fall 2012
Description:
In this course, the fundamentals of stochastic processes are examined, including topics such as random variables, statistical characteristics of processes at various orders, strictly and broadly stationary processes, cyclostationary processes, autocorrelation functions, ergodic processes, band-limited processes, sampling theory, and more.
Syllabus:
- Definition of Random Variable and Review of Probability Concepts
- Definition of Stochastic Processes and its General Concepts
- Statistical Characteristics of Random Variables in Different Orders
- Strict-Sense Stationary Process (SSS) and Wide-Sense Stationary Process (WSS), Cyclostationary Process
- AutoCorrelation Function Properties, Power Spectrum (Discrete-Time and Continues-Time Processes)
- Random Input Systems Analysis, Relationship Between Statistical Characteristics of Input and Output, Spectral Relativity of Input and Output of Linear Systems
- Ergodic Processes (Distribution Eng., Correlation Erg., Mean-Ergodic)
- Special Processes Analysis and their Applications
- White Noise, Thermal Noise, Wiener Process, Poisson Process, Shot Noise, PAM, Telegraph Signal
- Detection of Deterministic Signals in White and Color Noise, Matched Filter, Hilbert Transform
- Narrowband Processes and Sampling Theory
- Karhunen-Loeve (KL) Expansion and Fourier Series as a Special Case of KL
- Factorization and Innovations
- Mean Square Linear Estimation
- Regular and Predictable Process
- Smoothing (Discrete-Time and Continuous-Time Processes)
- Prediction (Discrete-Time and Continuous-Time Processes)
- Filtering and Prediction (Discrete-Time and Continuous-Time Processes)
- Estimation of a Regular Stationary Signal in White Noise as a Special Case
- Estimation of a Stationary Autoregressive Process
- Kalman Filtering for Discrete-Time Processes, Simplification of Kalman Filters for ARMA and AR Processes in White Noise
References:
- A. Papoulis, S. U. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, 2002
Last Update: 2024-07-09