Introduction
Description:• The course is designed to provide students an introduction to random
signals, their correlation functions and power spectra, and wide sense stationarity assumption in random signal modeling. Random processes/signals, play a very important role in the fields of communications, signal processing, and control.
• A solid background in probability and signal processing is needed. (Prerequisite: Probability and Signals and Systems)
Random Signals
Introduction
• Outline– Review of the Theory of Random Variables and Random Vectors
– Random Processes and Correlation Functions
– Stationarity and Ergodicity
– Review of Fourier Transforms
– Power Spectrum for WSS Signals
– LTI Systems with Random Inputs
– Gaussian and Poisson Processes, Poisson Impulses
– Noise (White: Thermal, Shot)
– Sampling of Random Processes, Bandlimited White Noise
Random Signals
Introduction
• References– Simon Haykin, “Communication Systems”, 4th edition,
– Leon W. Couch, II, “Digital and Analog Communication Systems”, 7th edition, Prentice Hall.
– John G. Proakis & Masoud Salehi, “Communication Systems Engineering, 2nd edition,
– Henry Stark & John W. Woods, “Probability, Random Processes with Applications to Signal Processing”, 3rd edition,
– Athanasios Papoulis, “Probability, Random Variables and Stochastic Processes”, 3rd edition.
– Dimitri P. Bertsekas & John N. Tsitsiklis, “Introduction to Probability”, 2nd edition.
– C.W. Therrien, “Discrete random signals and statistical signal processing”, 1992.
Random Signals
Introduction
• Definition: The ensemble or the family of time functions is called a random signal if for a fixed time instant t_k {x(t_k, s_i)} i=1,2,3,... constitutes a random variable (r.v.)
Random Signals
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