engineering recuitment GATE ECE 2023-24 Test Series Communication Systems Random Processes Correlation and Power Spectral Density
A bandlimited Gaussian white noise PSD is given by
\({{\rm{S}}_{{\rm{nn}}}}\left( {\rm{f}} \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{{{\rm{N}}_{\rm{o}}}}}{2};}&{\left| {\rm{f}} \right| \le {\rm{B}}}\\ {0{\rm{}}\ ;}&{{\rm{otherwise}}} \end{array}} \right.\)
The autocorrelation function \({{\rm{R}}_{{\rm{nn}}}}\left( {\rm{\tau }} \right)\) is
1
\(2{{\rm{N}}_{\rm{o}}}{\rm{Bsinc}}\left( {{\rm{B\tau }}} \right)\)
2
\({{\rm{N}}_{\rm{o}}}{\rm{Bsinc}}\left( {2{\rm{B\tau }}} \right)\)
3
\(2{{\rm{N}}_{\rm{o}}}{\rm{Bsinc}}\left( {2{\rm{\pi B\tau }}} \right)\)
4
\(2{{\rm{N}}_{\rm{o}}}{\rm{Bsinc}}\left( {2{\rm{B\tau }}} \right)\)