Hazırlayan
Random Signals
Chapter 1: Introduction
Yard. Doç. Dr. Tansu FİLİK
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
Random Signals
Introduction
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
Introduction
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals
Review of the Theory of Random Variables and Random
Vectors
Random Signals