If are the Fourier coefficients of a real signal, x(t), fill in all the steps to show

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If

х, %3D |X, |еxp[j/х,1

are the Fourier coefficients of a real signal, x(t),  fill in all the steps to show that:

(a) ||X„| = |X_„| and /X, = -/X_ -п

(b) Xn is a real, even function of n for x(t) even.

(c) Xn is imaginary and an odd function of n for x(t) odd. 

(d) x(t) = -x(t + T0/2) (half wave odd symmetry) implies that Xn = 0, n even.

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Related Book For  book-img-for-question

Principles of Communications Systems, Modulation and Noise

ISBN: 978-8126556793

7th edition

Authors: Rodger E. Ziemer, William H. Tranter

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