Definition | ||||||

The . Using the complex form of Cosine, we can easily prove that the above integral can be re-written as: .
The above integral can be expressed by the following Since is a dummy variable, we can replace it with and define the Fourier transform of and its inverse transform as:
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where and are the Fourier and its inverse transform operators, respectively. |

Fourier Cosine and Sine Transforms | |

If is an | |

where is called the On the other hand, if is an | |

where is called the |