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LaplaceTransformFourierSinTransform

FourierTransform

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

FilledSmallSquareFourierTransform[expr, , , ... , , , ... ] gives the multidimensional Fourier transform of expr.

FilledSmallSquare The Fourier transform of a function is by default defined to be .

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 Fourier transform computed by FourierTransform 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 FourierTransform.

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

FilledSmallSquare In TraditionalForm, FourierTransform is output using .

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

FilledSmallSquare See also: FourierSinTransform, FourierCosTransform, Fourier, InverseFourierTransform, LaplaceTransform, Integrate.

Further Examples

LaplaceTransformFourierSinTransform