Channel Lowpass Impulse Response(2/2) v(t)represents the complex envelope of the received signal: v()-p.-u6-t)ct) i=l .u(t-t)=tutd(well known property of the 8-distribution) ↓ 60-2了能-f-gea--j2,c-ta0u6- k0=2p6t-4)4w网 Channel lowpass impulse response h个 v()-.G)w6-5)-Jb(-)uG)-h.()out)Channel Lowpass Impulse Response (2/2) ( ) ( ) ( ) ∑ = θ − π ⋅ = ρ ⋅ − ⋅ r i 0 i N i 1 j 2 f t i i v t u t t e  (well known property of the ( ) ( ) ( ) δ-distribution) ∫ ∞ −∞ u t − t = δ ξ − t ⋅u t − ξ dξ i i ( ) ( ) ( ) ( ) ( ) ( ) ( ) ∑ ∫ ∫ ∑ ∞ −∞ = θ − π ⋅ = θ − π ⋅ ∞ −∞ v t = ρ δ ξ − t ⋅u t − ξ dξ⋅e = ρ δ ξ − t e u t − ξ dξ r i 0 i r i 0 i N i 1 j 2 f t i i N i 1 j 2 f t i i  v(t) represents the complex envelope of the received signal: h0 (t) ≡ ρi δ t − t ( i)ej θi−2π f0⋅t ( i) i=1 Nr ∑ v(t) h ( ) u(t )d h (t ) u( )d h (t) u(t) = ∫ 0 ξ ⋅ − ξ ξ = ∫ 0 − ξ ⋅ ξ ξ = 0 ⊗ ∞ −∞ ∞ −∞ |h0| t ti ρi Channel lowpass impulse response