wavelet

mathematics A waveform that is bounded in both frequency

and duration. Wavelet tranforms provide an alternative to

more traditional Fourier transforms used for analysing

waveforms, e.g. sound.

The Fourier transform converts a signal into a continuous

series of sine waves, each of which is of constant frequency

and amplitude and of infinite duration. In contrast, most

real-world signals (such as music or images) have a finite

duration and abrupt changes in frequency.

Wavelet transforms convert a signal into a series of wavelets.

In theory, signals processed by the wavelet transform can be

stored more efficiently than ones processed by Fourier

transform. Wavelets can also be constructed with rough edges,

to better approximate real-world signals.

For example, the United States Federal Bureau of Investigation

found that Fourier transforms proved inefficient for

approximating the whorls of fingerprints but a wavelet

transform resulted in crisper reconstructed images.

SBG Austria .

["Ten Lectures on Wavelets", Ingrid Daubechies].

(1994-11-09)