Ondelette

A ondelette ( wavelet in English) is a mathematical kind of Fonction which is used to break up a function or a signal into various frequential components with a resolution adapted to their scale. A transform in ondelettes is the representation of a function by ondelettes. The ondelettes known as “girls” are shifted copies ou/et lengthened/compressed of a ondelette known as “mother”. These different ondelettes each one is dedicated to the analysis of a precise part of the function or signal. The advantage of the ondelettes on the Transformée of Fourier is that they allow a better analysis of the functions presenting of discontinuities or the peaks.

The transforms in ondelette are divided into two categories:

  • the transformed into ondelettes discrete ( TOD or DWT ) which use a specific whole of shifts/compressions

  • the transformed into ondelettes continues ( FAKE or CWT ) which work on the whole of the possible shifts/compressions

The term of ondelette was introduced by Jean Morlet and Alex Grossman at the beginning of the Années 1980. Initially French term, it was then translated into English by wavelet , with the term wave (wave) and the diminutive let (small).

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