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InverseFourierTransform

InverseFourierTransform

gives the symbolic inverse Fourier transform of expr.

InverseFourierTransform

gives the multidimensional inverse Fourier transform of expr.

MORE INFORMATION

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

Other definitions are used in some scientific and technical fields.

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

With the setting FourierParameters the inverse Fourier transform computed by InverseFourierTransform is .

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

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

InverseFourierTransform 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.

In TraditionalForm, InverseFourierTransform is output using .

Basic Examples (2)

Out[1]=

Out[1]=

Out[2]=

Elementary functions:

Special functions:

Piecewise functions and distributions:

TraditionalForm formatting:

Generalizations & Extensions (1)

Multidimensional inverse Fourier transform:

The inverse Fourier transform of BesselJ is a piecewise function:

Default modern physics convention:

Convention for pure mathematics and systems engineering:

Convention for classical physics:

Convention for signal processing:

Use GenerateConditions->True to get parameter conditions for when a result is valid:

Properties & Relations (3)

InverseFourierTransform and FourierTransform are mutual inverses:

InverseFourierTransform and InverseFourierCosTransform are equal for even functions:

InverseFourierTransform and InverseFourierSinTransform differ by

for odd functions:

Possible Issues (1)

The result from an inverse Fourier transform may not have the same form as the original:

Neat Examples (1)

The InverseFourierTransform of

is a

convolution of box functions:

InverseFourierSinTransform InverseFourierCosTransform InverseFourier FourierTransform InverseFourierSequenceTransform Convolve InverseLaplaceTransform Integrate

Integral Transforms and Related Operations

Fourier Analysis

Integral Transforms

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