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wavelet
(redirected from Wavelet analysis)

   Also found in: Wikipedia 0.02 sec.
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.

(mathematics)wavelet - 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].


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Chapter 4 continues in a partially similar vein, but here less familiar methods of time series analysis such as phase spectra, complex demodulation, wavelet analysis and singular spectrum analysis are presented.
For a healthy heart, these correlations appear as arches in plots displaying the wavelet analysis (bottom).
5 cms There were 32* Patients positive for breast cancer Cancers found by mammography 25** Cancers found by Lifeline's First Warning System(TM)(FWS): Neural net analysis 30*** Wavelet analysis 31 Wavelet/neural net analysis 32 * Four cancers in the series were eliminated from consideration by either statistical or neural network because of bad data.
 
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