# Definitions for inverse fourier transformin·verse fourier trans·form

### WiktionaryRate this definition:5.0 / 1 vote

1. inverse Fourier transformnoun

A mathematical operation that transforms a function for a discrete or continuous spectrum into a function for the amplitude with the given spectrum; an inverse transform of the Fourier transform.

### WikipediaRate this definition:0.0 / 0 votes

1. inverse fourier transform

In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency and phase information about a wave then we may reconstruct the original wave precisely. The theorem says that if we have a function f : R → C {\displaystyle f:\mathbb {R} \to \mathbb {C} } satisfying certain conditions, and we use the convention for the Fourier transform that ( F f ) ( ξ ) := ∫ R e − 2 π i y ⋅ ξ f ( y ) d y , {\displaystyle ({\mathcal {F}}f)(\xi ):=\int _{\mathbb {R} }e^{-2\pi iy\cdot \xi }\,f(y)\,dy,} then f ( x ) = ∫ R e 2 π i x ⋅ ξ ( F f ) ( ξ ) d ξ . {\displaystyle f(x)=\int _{\mathbb {R} }e^{2\pi ix\cdot \xi }\,({\mathcal {F}}f)(\xi )\,d\xi .} In other words, the theorem says that f ( x ) = ∬ R 2 e 2 π i ( x − y ) ⋅ ξ f ( y ) d y d ξ . {\displaystyle f(x)=\iint _{\mathbb {R} ^{2}}e^{2\pi i(x-y)\cdot \xi }\,f(y)\,dy\,d\xi .} This last equation is called the Fourier integral theorem. Another way to state the theorem is that if R {\displaystyle R} is the flip operator i.e. ( R f ) ( x ) := f ( − x ) {\displaystyle (Rf)(x):=f(-x)} , then F − 1 = F R = R F . {\displaystyle {\mathcal {F}}^{-1}={\mathcal {F}}R=R{\mathcal {F}}.} The theorem holds if both f {\displaystyle f} and its Fourier transform are absolutely integrable (in the Lebesgue sense) and f {\displaystyle f} is continuous at the point x {\displaystyle x} . However, even under more general conditions versions of the Fourier inversion theorem hold. In these cases the integrals above may not converge in an ordinary sense.

### Numerology

1. Chaldean Numerology

The numerical value of inverse fourier transform in Chaldean Numerology is: 4

2. Pythagorean Numerology

The numerical value of inverse fourier transform in Pythagorean Numerology is: 2

## Translations for inverse fourier transform

### From our Multilingual Translation Dictionary

• उलटा फूरियर रूपांतरण

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"inverse fourier transform." Definitions.net. STANDS4 LLC, 2023. Web. 29 May 2023. <https://www.definitions.net/definition/inverse+fourier+transform>.

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