EE3008_Lecture7_supplementary_note

EE3008_Lecture7_supplementary_note - 1 Derivation of Power...

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1 Derivation of Power Spectrums of Digital Baseband & Bandpass Modulated Signals Department of Electronic Engineering EE3008 Principles of Communications Lecture 7
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2 1. Power Spectrum of Digital Baseband Modulated Signal For a digital baseband modulated signal ( ) ( ), n n s t Z v t n τ = −∞ = where v ( t ) is a baseband signal and variable, the power spectrum of s ( t ) is 2 2 2 1 ( ) | ( ) | Z s Z n n G f V f f μ σ δ τ τ τ = −∞ = + Z n =Z is a discrete random Department of Electronic Engineering EE3008 Principles of Communications Lecture 7
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3 The mean and autocorrelation of s ( t ) are given by E [ s ( t )] = E [ Z n ] n = −∞ v ( t n τ ) = μ z v ( t n τ ) n = −∞ respectively. Note that both of them are periodic with period τ . and ( , ) [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) s m n m n Z m n Z n m R t x t E Z Z v t m v t x n R n m v t m v t x n R n v t m v t x m n τ τ τ τ τ τ τ = −∞ = −∞ = −∞ = −∞ = −∞ = −∞ + = + = + = + ∑ ∑
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