Show that the PSD function of a WSS random process ({X}) satisfies the following properties: (a) (Gamma_{X}(0)=sum_{v=-infty}^{infty}

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Show that the PSD function of a WSS random process \(\{X\}\) satisfies the following properties:

(a) \(\Gamma_{X}(0)=\sum_{v=-\infty}^{\infty} R_{X}(v)\).

(b) It is an even function; that is: \(\Gamma_{X}\left(\mathrm{e}^{\mathrm{j} \omega}\right)=\Gamma_{X}\left(\mathrm{e}^{-\mathrm{j} \omega}\right)\), for all \(\omega\).

(c) It is a nonnegative function; that is: \(\Gamma_{X}\left(\mathrm{e}^{\mathrm{j} \omega}\right) \geq 0\), for all \(\omega\).

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Digital Signal Processing System Analysis And Design

ISBN: 9780521887755

2nd Edition

Authors: Paulo S. R. Diniz, Eduardo A. B. Da Silva , Sergio L. Netto

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