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 ${\displaystyle t}$) ar tasɣent n umutti asemlal ${\displaystyle s}$.

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.

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

${\displaystyle F(x)=\int _{0}^{+\infty }{f(t)*e^{-st}dt}$

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

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 :

${\displaystyle F(x)=\int _{-\infty }^{+\infty }{f(t)*e^{-st}dt}$