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Let x(1) and y(t) be two signals; then the correlation function is defined as $ry(1) = x(1 + 7)y(7)dr. The function &x(1) is usually referred to as the autocorrelation function of the signal x(1), while ø»(1) is often called a cross-correlation function. (a) What is the relationship between ø,y(t) and ¢y»(t)? (b) Compute the odd part of øx.(1). (c) Suppose that y(1) = x(t + T). Express ,,(t) and øyy(1) in terms of 4«(1). %3D

Let x(1) and y(t) be two signals; then the correlation function is defined as $ry(1) = x(1 + 7)y(7)dr. The function &x(1) is usually referred to as the autocorrelation function of the signal x(1), while ø»(1) is often called a cross-correlation function. (a) What is the relationship between ø,y(t) and ¢y»(t)? (b) Compute the odd part of øx.(1). (c) Suppose that y(1) = x(t + T). Express ,,(t) and øyy(1) in terms of 4«(1). %3D

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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1.37. An important concept in many communications applications is the correlation be- tween two signals. In the problems at the end of Chapter 2, we will have more to say about this topic and will provide some indication of how it is used in practice. For now, we content ourselves with a brief introduction to correlation functions and some of their properties. Let x(t) and y(1) be two signals; then the correlation function is defined as - L. b1,(1) = x(1 + T)y(7)dT. The function ,u(1) is usually referred to as the autocorrelation function of the signal x(t), while oy(t) is often called a cross-correlation function. (a) What is the relationship between 4,y(1) and øy»(1)? (b) Compute the odd part of øx:(1). (c) Suppose that y(t) = x(t + T). Express ,,(1) and Þyy(1) in terms of p«(1).
Transcribed Image Text:1.37. An important concept in many communications applications is the correlation be- tween two signals. In the problems at the end of Chapter 2, we will have more to say about this topic and will provide some indication of how it is used in practice. For now, we content ourselves with a brief introduction to correlation functions and some of their properties. Let x(t) and y(1) be two signals; then the correlation function is defined as - L. b1,(1) = x(1 + T)y(7)dT. The function ,u(1) is usually referred to as the autocorrelation function of the signal x(t), while oy(t) is often called a cross-correlation function. (a) What is the relationship between 4,y(1) and øy»(1)? (b) Compute the odd part of øx:(1). (c) Suppose that y(t) = x(t + T). Express ,,(1) and Þyy(1) in terms of p«(1).
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