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 UnitStep

 http://functions.wolfram.com/14.01.22.0001.01

 Input Form

 FourierTransform[UnitStep[t], t, x] == I/(Sqrt[2 Pi] x) + Sqrt[Pi/2] DiracDelta[x]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["FourierTransform", "[", RowBox[List[RowBox[List["UnitStep", "[", "t", "]"]], ",", "t", ",", "x"]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[ImaginaryI]", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", "x"]]], "+", RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["DiracDelta", "[", "x", "]"]]]]]]]]]]

 MathML Form

 t [ θ UnitStep ( t ) ] ( x ) 2 π x + π 2 δ DiracDelta ( x ) FourierTransform UnitStep t t x 2 1 2 x -1 2 -1 1 2 DiracDelta x [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FourierTransform", "[", RowBox[List[RowBox[List["UnitStep", "[", "t_", "]"]], ",", "t_", ",", "x_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["\[ImaginaryI]", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", "x"]]], "+", RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["DiracDelta", "[", "x", "]"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29

© 1998-2013 Wolfram Research, Inc.