Question: 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
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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