Genesis of wavelet transform types and applications

N. Sundararajan, N. Vasudha

Research output: Chapter in Book/Report/Conference proceedingChapter


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
Number of pages24
ISBN (Electronic)9781466553606
ISBN (Print)9781466553590
Publication statusPublished - Jan 1 2013

ASJC Scopus subject areas

  • General Earth and Planetary Sciences
  • General Physics and Astronomy


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