Téoréma sampling

Transmisi digital sinyal analog dimungkinkeun ku jasana téorema sampling.

Conto sinyal nu disampling

Sinyal pita kawates

Spéktrum hiji sinyal pita kawates sabagé fungsi ti frékuénsi

Sinyal pita kawates nyaéta hiji sinyal m(t) nu transformasi Fourierna sarua jeung enol di saluhureun hiji frékuénsi $\omega _{M}$ tinangtu:

$m(t)\quad {\stackrel {\mathcal {F}}{\Longleftrightarrow }}\quad M(\omega )=0$ pikeun $|\omega |>\omega _{M}=2\pi f_{M}$ ....... (1)

Téorema sampling

Lamun hiji sinyal m(t) mangrupa hiji sinyal pita kawates nu boga haga ril nu luyu jeung parsamaan (1), mangka m(t) sacara unik bisa ditangtukeun ti harga-harga m(t) anu dicokot contona (disampel) dina interval-interval waktu nu saragem $T_{s}[\leq (1/2f_{M})]$. Dina kanyataanana m(t) dinyatakeun ku:

$m(t)=\sum _{-\infty }^{\infty }m(nT_{s}){\frac {\sin \omega _{M}(t-nT_{s})}{\omega _{M}(t-nT_{s})}}.$

di mana T_s mangrupa périoda sampling sarta kabalikanana f_s = 1/T_s salaku laju sampling.

Jadi, téoréma sampling nganyatakeun yén hiji sinyal pita kawates nu teu boga komponén frékuénsi leuwih luhur ti f_M Hz bisa ditimukeun deui sagemblengna tina sakumpulan conto (sampel) anu dicokot dina laju $f_{s}(\geq f_{M})$ sampel per detik.

Téoréma sampling di luhur mindeng disebut uniform sampling theorem pikeun sinyal pita dasar (baseband) atawa sinyal low pass.

Laju sampling minimum, 2f_M sampel per detik, disebut laju Nyquist; kabalikanana 1/(2f_M) (nu diukur dina detik) disebut interval Nyquist

Tempo ogé

• Sampling
• Sinyal

Rujukan

1. Hsu, Hwei P., Schaum's Outline of Théory and Problems of Analog and Digital Communications, McGraw Hill, 1993

Tumbu ka luar

• Learning by Simulations Interactive simulation of the effects of inadequate sampling
• Undersampling and an application of it
• Sampling Theory For Digital Audio Archived 2006-06-14 di Wayback Machine
• Journal devoted to Sampling Theory