The two-frequency correlation function x (N, ) is often used in radar and sonar to evaluate

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The two-frequency correlation function Ф_x(N, ω) is often used in radar and sonar to evaluate the frequency and travel-time resolution of a signal. For discrete-time signals, we define

x[n+ N]x*[n – N]e¬jom Ox{N, w) = %3D n=-00 (a) Show that Ox(-N. -w) = 0;(N, w). (b) If 0 < a < 1, x[n] = Aa

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Discrete Time Signal Processing

ISBN: 978-0137549207

2nd Edition

Authors: Alan V. Oppenheim, Rolan W. Schafer

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Question Posted: May 26, 2011 02:55 AM

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The two-frequency correlation function x (N, ) is often used in radar and sonar to evaluate

Question:

x[n+ N]x*[n – N]e¬jom Ox{N, w) = %3D n=-00 (a) Show that Ox(-N. -w) = 0;(N, w). (b) If 0 < a < 1, x[n] = Aa"u[n], find O;(N, w). (Assume that N 2 0.) (c) The function O;(N, w) has a frequency domain dual. Show that x (elv+(w/2}!) x* (e'lv-(w/2))ei2uNdv. Ox(N, w) = 2л %3D

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Discrete Time Signal Processing

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x[n+ N]x[n – N]e¬jom Ox{N, w) = %3D n=-00 (a) Show that Ox(-N. -w) = 0;(N, w). (b) If 0 < a < 1, x[n] = Aa"u[n], find O;(N, w). (Assume that N 2 0.) (c) The function O;(N, w) has a frequency domain dual. Show that x (elv+(w/2}!) x (e'lv-(w/2))ei2uNdv. Ox(N, w) = 2л %3D