Genesis of wavelet transform types and applications

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish
Title of host publicationWavelets and Fractals in Earth System Sciences
PublisherCRC Press
Pages93-116
Number of pages24
ISBN (Electronic)9781466553606
ISBN (Print)9781466553590
DOIs
Publication statusPublished - Jan 1 2013

Fingerprint

integral transformations
wavelet analysis
wavelet
transform
histories
Mellin transforms
radon
strings
engineering
thermodynamics
oscillations
Fourier transform
Radon transform
Laplace transform
history
oscillation

ASJC Scopus subject areas

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

Cite this

Sundararajan, N., & Vasudha, N. (2013). Genesis of wavelet transform types and applications. In 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.

Wavelets and Fractals in Earth System Sciences. CRC Press, 2013. p. 93-116.

Research output: Chapter in Book/Report/Conference proceedingChapter

Sundararajan, N & Vasudha, N 2013, Genesis of wavelet transform types and applications. in Wavelets and Fractals in Earth System Sciences. CRC Press, pp. 93-116. https://doi.org/10.1201/b16046
Sundararajan N, Vasudha N. Genesis of wavelet transform types and applications. In Wavelets and Fractals in Earth System Sciences. CRC Press. 2013. p. 93-116 https://doi.org/10.1201/b16046
Sundararajan, Narasimman ; Vasudha, N. / Genesis of wavelet transform types and applications. Wavelets and Fractals in Earth System Sciences. CRC Press, 2013. pp. 93-116
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