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

ASJC Scopus subject areas

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

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    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