Let H denote the (ideal) operation of Hilbert transformation that is, Prove the following properties of the ideal Hilbert transform operator Hx n x k h n k , u x H k o0 where h n is 2 sin (rn 2) h n 0, n 0 n 0 (a) H H x n x(n x n H x n ) 0 (b) n 00 (c) H x n y n H(x n y n x n H y n , wherex n and y...

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Let H{?} denote the (ideal) operation of Hilbert transformation; that is, Prove the following properties of the

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Let H{?} denote the (ideal) operation of Hilbert transformation; that is,

Prove the following properties of the ideal Hilbert transform operator.

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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 02:57 AM

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Let H{?} denote the (ideal) operation of Hilbert transformation; that is, Prove the following properties of the

Question:

Hx[n}} = x[k]h[n - k], [[u]x}H k=-o0 where h[n] is 2 sin (rn/2) h[n] = 0, n+0. n = 0. (a) H{H{x[n]]] = -x(n] x[n]H{x[n]) = 0 (b) n=-00 (c) H{x[n]+y[n]} = H(x[n]}*y[n] = x[n]+H{y[n]}, wherex[n]and y[n] are any sequences. %3D

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Discrete Time Signal Processing

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