What does inverse fourier transform mean?

Definitions for inverse fourier transform
in·verse fourier trans·form

This dictionary definitions page includes all the possible meanings, example usage and translations of the word inverse fourier transform.


  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.


  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.

How to pronounce inverse fourier transform?

How to say inverse fourier transform in sign language?


  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 रूपांतरणHindi

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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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