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InverseLaplaceTransformInverseFourierSinTransform

InverseFourierTransform

FilledSmallSquareInverseFourierTransform[expr, , t] gives the symbolic inverse Fourier transform of expr.

FilledSmallSquareInverseFourierTransform[expr, , , ... , , , ... ] gives the multidimensional inverse Fourier transform of expr.

FilledSmallSquare The inverse Fourier transform of a function is by default defined as .

FilledSmallSquare Other definitions are used in some scientific and technical fields.

FilledSmallSquare Different choices of definitions can be specified using the option FourierParameters.

FilledSmallSquare With the setting FourierParameters->a, b the inverse Fourier transform computed by InverseFourierTransform is .

FilledSmallSquare Some common choices for a, b are {0, 1} (default; modern physics), {1, -1} (pure mathematics; systems engineering), {-1, 1} (classical physics), {0, -2 Pi} (signal processing).

FilledSmallSquareAssumptions and other options to Integrate can also be given in InverseFourierTransform.

FilledSmallSquareInverseFourierTransform[expr, , t] yields an expression depending on the continuous variable t that represents the symbolic inverse Fourier transform of expr with respect to the continuous variable . InverseFourier[list] takes a finite list of numbers as input, and yields as output a list representing the discrete inverse Fourier transform of the input.

FilledSmallSquare In TraditionalForm, InverseFourierTransform is output using .

FilledSmallSquare See The Mathematica Book: Section 1.5.11 and Section 3.5.11.

FilledSmallSquare See also: InverseFourierSinTransform, InverseFourierCosTransform, InverseFourier, FourierTransform, InverseLaplaceTransform, Integrate.

Further Examples

InverseLaplaceTransformInverseFourierSinTransform