An important concept in many communications applications is the correlation between two
Chapter 1, Problem 1.37(choose chapter or problem)
An important concept in many communications applications is the correlation between 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(t) be two signals; then the correlation function is defined as "'""(!) = r~ x(t + T)y( T)dT. The function xxCt) is usually referred to as the autocorrelation function of the signal x(t), while xy(t) is often called a cross-correlation function. (a) What is the relationship between xy(t) and yx(t)? (b) Compute the odd part of xxU). (c) Suppose that y(t) = x(t + T). Express xy(t) and yy(t) in terms of xx(t).
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