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IEVref: | 103-04-01 | ID: | |

Language: | en | Status: Standard | |

Term: | Fourier transform | ||

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Definition: | for a real or complex function f(t) of the real variable t, complex function $F(\omega )$ of the real variable ω, given by the integral transformation $F(\omega )={\int}_{\text{\hspace{0.05em}}-\infty}^{\text{\hspace{0.05em}}+\infty}f(t){e}^{-\text{j}\omega \text{\hspace{0.05em}}t}\mathrm{d}t$ where j is the imaginary unit Note 1 to entry: If Note 2 to entry: The Fourier transform of the function | ||

Publication date: | 2009-12 | ||

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Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00020 (IEV 103) - evaluation. JGO | ||

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$F(\omega )={\int}_{\text{\hspace{0.05em}}-\infty}^{\text{\hspace{0.05em}}+\infty}f(t){e}^{-\text{j}\omega \text{\hspace{0.05em}}t}\mathrm{d}t$

where j is the imaginary unit

Note 1 to entry: If *t* is time, the variable *ω* represents angular frequency.

Note 2 to entry: The Fourier transform of the function *f* is also denoted F*f* or ℱ*f*.