Figure shows three periodic sequences x 1 [n] through x 3 [n]. These sequences can be expressed

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Figure shows three periodic sequences x1[n] through x3[n]. These sequences can be expressed in a Fourier series as

(a) For which sequences can the time origin be chosen such that all the X[k] are real?

(b) For which sequences can the time origin be chosen such that all the X[k] (except for k an integer multiple of N) are imaginary?

(c) For which sequences does X[k] = 0 for k = ? 2, ? 4, ? 6?

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Discrete Time Signal Processing

ISBN: 978-0137549207

2nd Edition

Authors: Alan V. Oppenheim, Rolan W. Schafer

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