Tabeddilt n Laplaṣ

Deg tusnakt, Tabeddilt n Laplaṣ, tettwasemma-d ɣef Pierre-Simon Laplace , d tabeddilt tuɣridt, i d smutti n tesɣent n umutti ilaw ( s tuget t {\displaystyle t} ) ar tasɣent n umutti asemlal s {\displaystyle s} .

Amezruy

Tabeddilt n Laplaṣ tewwi isem-is seg umusnak afransis Pierre-Simon Laplaṣe (1749-1827). Laplaṣe yessiweḍ ad d-yefk tabadut n tbeddilt-agi deg useggas n 1785, mi yella yeţţnadi ɣef tlufa n tmikanikt tagennawt. Seg yimir-nni, tabeddilt n Laplaṣ tuɣal d allal aseklan deg waṭas n yiḥricen n tusnakt d tussna.

Tabadut tamsalɣa

Tabeddilt n Laplaṣ n tesɣent f ( t ) {\displaystyle f(t)} , yettwasbedun i wakk imḍanen ilawen t ≥ 0 {\displaystyle t\geq 0} , d nettat d tesɣunt F ( t ) {\displaystyle F(t)} am akka:

F ( x ) = ∫ 0 + ∞ f ( t ) ∗ e − s t d t {\displaystyle F(x)=\int _{0}^{+\infty }{f(t)*e^{-st}}dt}

anda : s = σ + i ω , {\displaystyle s=\sigma +i\omega ,}

Tabeddilt n Laplaṣ n sin idisen

ma neqqar "tabeddilt n Laplaṣ" akken s tḥerfit, ad negg srid tabeddilt n Laplaṣ n yiwen idis i t-nezwar deg uḥric amezwaru (seg yilem ar ifeḍ n ufella). Ama yella useɣzef n tbeddilt agi akken ad yecmel akk imḍanen ilawen seg yifeḍ n wadda ar ifeḍ n ufella, wagi neqqar-as "Tabeddilt n Laplaṣ n sin idisen".

Tabedddilt n Laplaṣ n sin idisen tettwasbedu am akka :

F ( x ) = ∫ − ∞ + ∞ f ( t ) ∗ e − s t d t {\displaystyle F(x)=\int _{-\infty }^{+\infty }{f(t)*e^{-st}}dt}