### 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 |

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### ASJC Scopus subject areas

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

### Cite this

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

**Genesis of wavelet transform types and applications.** / Sundararajan, Narasimman; Vasudha, N.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Genesis of wavelet transform types and applications

AU - Sundararajan, Narasimman

AU - Vasudha, N.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

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U2 - 10.1201/b16046

DO - 10.1201/b16046

M3 - Chapter

SN - 9781466553590

SP - 93

EP - 116

BT - Wavelets and Fractals in Earth System Sciences

PB - CRC Press

ER -