The autocorrelation function of a signal x(t) is defined as cf>xx(T) = J:oo
Chapter 9, Problem 9.61(choose chapter or problem)
The autocorrelation function of a signal x(t) is defined as cf>xx(T) = J:oo X(t)x(t+T)dt. (a) Determine, in terms of x(t), the impulse response h(t) of an LTI system for which, when the input is x(t), the output is cf>xAt) [Figure P9.61(a)]. (b) From your answer in part (a), determine xx(s), the Laplace transform of cf>xA T) in terms of X(s). Also, express xxUw), the Fourier transform of cf>xx(T), in terms of X(jw ). (c) If X(s) has the pole-zero pattern and ROC shown in Figure P9.61(b), sketch the pole-zero pattern and indicate the ROC for xx
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