wavelet

[′wāv·lət] (mathematics) One of a collection of mathematical functions that serve as the elementary building blocks of a mathematical tool for analyzing and synthesizing functions, and for forming representations of signals in both time and frequency.

wavelet

A small shock wave, usually present in large numbers in boundary layers and around the surface of a supersonic body. Also called a Mach wave or a Mach wavelet

wavelet

(mathematics)A waveform that is bounded in both frequencyand duration. Wavelet tranforms provide an alternative tomore traditional Fourier transforms used for analysingwaveforms, e.g. sound.

The Fourier transform converts a signal into a continuousseries of sine waves, each of which is of constant frequencyand amplitude and of infinite duration. In contrast, mostreal-world signals (such as music or images) have a finiteduration and abrupt changes in frequency.

Wavelet transforms convert a signal into a series of wavelets.In theory, signals processed by the wavelet transform can bestored more efficiently than ones processed by Fouriertransform. Wavelets can also be constructed with rough edges,to better approximate real-world signals.

For example, the United States Federal Bureau of Investigationfound that Fourier transforms proved inefficient forapproximating the whorls of fingerprints but a wavelettransform resulted in crisper reconstructed images.

SBG Austria.

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

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Synonyms for wavelet

noun a small wave on the surface of a liquid

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