Natural Sampling

×)(tg

( )tp

Periodic gate function ( ) is used as sampling function, which has a freq. spectrum.

=nP

t-T T

…. ….

τ

( )tp

….. ω…..

Fourier series coefficients of p(t)

( ) =tg s

( ) =ωsG

( ) =tp

Flat-Top Sampling

×)(tg

( ) ∑∞

−∞=−=

nsT nTtt

s)(δδ

( )tgPAM

( ) ( ) ( )∑∞

−∞=−=

nsss nTtnTgtg δ

( ) =tgPAM ( ) =ωPAMG

( ) ∑∞

−∞=

−=

n sss T

nG

TG

πωπω 22

Time-domain Frequency-domain

The resulting signal from flat-top sampling is known as “Pulse Amplitude Modulated” (PAM) signal.

Q(w)g(t) Ideal Time-

Sampling

@ ws ≥ 2W

gPAM(t)gs(t) g(t)Equalizer

P(w)= 1/Q(w)LPFW

gs(t)gPAM(t)

Reconstruction of original signal from flat-top sampling

( ) =ωQ

t0-τ/2 τ/2

A

( ) ( )τtrectAtq =

t0 τ

A

( )

−=

ττ 2/t

rectAtq

( ) =ωQ

Equalization:

Flat-top sampling introduces both amplitude-distortion and/or phase-distortion.

Comparison of ideal, natural and flat-top sampling methods

fs = 1/Ts ≥ 2fm

g(t)ideal

natural

flat-top

Ts

•

•

•

Path loss and noise Amplification

Path loss and noise Regeneration

Amplification vs. Regeneration•