# wavelet

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## 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 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].
References in periodicals archive ?
In the above equation, i and j denote, respectively, the scale and the place in wavelet space.
After the ICA processing, useful fault sources has been extracted and are prepared for the Wavelet analysis.
The parameters of interest in this paper are the type and length of the wavelet filter, the number of levels in the wavelet decomposition, and the type of coding scheme used.
Where [psi](t) is the Wavelet function and s(t) a real signal.
The wavelet analysis involves transformation of a data series with a wavelet, a localized wave.
Sin embargo, la multiplexacion por division de paquetes wavelet (WPDM) (Wong et al.
The signal processing techniques employed which is the Fast Fourier Transform (FFT) and Wavelet Analysis (WA) provided in the MATLAB Software.
Discussing aspects of the theory of harmonic analysis and its applications, Arfaoui, Rezgui, and Mabrouk contribute to the reference on orthogonal polynomials, homogenous polynomials, and wavelet spheroidal analysis.
Conclusion: Wavelet decomposition-based template matching technique achieved satisfactory delineation of normal and arrhythmic electrocardiogram dynamics.
Later, to overcome the drawback of the DCT Wavelet transform is introduced which eliminate this drawback effectively.

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