Transcription of An Introduction to Wavelets
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An Introduction to Wavelets
An Introduction to WaveletsAmara GrapsABSTRACT. Wavelets are mathematical functions that cut up data into di erent frequency com-ponents, and then study each component with a resolution matched to its scale. They have ad-vantages over traditional Fourier methods in analyzing physical situations where the signal containsdiscontinuities and sharp spikes. Wavelets were developed independently in the elds of mathemat-ics, quantum physics, electrical engineering, and seismic geology. Interchanges between these eldsduring the last ten years have led to many newwavelet applications such as image compression,turbulence, human vision, radar, and earthquake prediction. This paper introduceswavelets to theinterested technical person outside of the digital signal processing eld. I describe the history ofwavelets beginning with Fourier, comparewavelet transforms with Fourier transforms, state prop-erties and other special aspects ofwavelets, and nish with some interesting applications such asimage compression, musical tones, and de-noising noisy OVERVIEWThe fundamental idea behindwavelets is to analyze according to scale.
The wavelet analysis procedure is to adopt a wavelet prototype function, called an analyzing wavelet or mother wavelet. Temporal analysis is performed with a contracted, high-frequency version of the prototype wavelet, while frequency analysis is performed with a dilated, low-frequency version of the same wavelet.
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