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