### Abstract

The history of integral transforms began with D’Alembert in 1747. He described the oscillations of a violin string using a superposition of sine functions. Fourier proposed a similar idea for heat equations in 1807 and formulated the elegant mathematical tool—the Fourier transform (FT), which marked the beginning of the modern history of integral transforms. It serves as a benchmark for validating the existence of other well-known integral transforms such as the z-transform, the Hartley transform, the Walsh transform, the Laplace transform, the Hankel transform, the Mellin transform, the Hilbert transform, and the Radon transform. They all have a wide range of applications in a variety of fields in science and engineering and are invariably related to FT.

Original language | English |
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Title of host publication | Wavelets and Fractals in Earth System Sciences |

Publisher | CRC Press |

Pages | 93-116 |

Number of pages | 24 |

ISBN (Electronic) | 9781466553606 |

ISBN (Print) | 9781466553590 |

DOIs | |

Publication status | Published - Jan 1 2013 |

### ASJC Scopus subject areas

- Earth and Planetary Sciences(all)
- Physics and Astronomy(all)

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## Cite this

*Wavelets and Fractals in Earth System Sciences*(pp. 93-116). CRC Press. https://doi.org/10.1201/b16046