EE3008_Lecture8_supplementary_note

EE3008_Lecture8_supplementary_note - 1 Variance of Sampled...

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Variance of Sampled AWGN 1 Department of Electronic Engineering EE3008 Principles of Communications Lecture 8
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2 Consider that AWGN n ( t ) passes through a filter h ( t ) and is sampled at t 0 . Suppose that the two-sided power spectral density of n ( t ) is N 0 /2 and the sampled noise . n o ( t 0 ) N (0, σ 0 2 ) Department of Electronic Engineering EE3008 Principles of Communications Lecture 8
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Unformatted text preview: According to and , n o ( t ) = n ( x ) h ( t − x ) dx t ∫ = N 2 δ ( x − t ) t ∫ t ∫ h ( t − x ) h ( t − t ) dxdt 2 = E[ n o 2 ( t )] we have 2 = E[ n ( x ) n ( t )] t ∫ t ∫ h ( t − x ) h ( t − t ) dxdt = N 2 h 2 ( t − x ) t ∫ dx ( ) ( ) 2 n N R τδ τ =...
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