Transcription of An Introduction to Wavelets - University of Delaware
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An Introduction to Wavelets - University of Delaware
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.
A basis function varies in scale by chopping up the same function or data space using difierent scale sizes. For example, imagine we have a signal over the domain from 0 to 1. We can divide the signal with two step functions that range from 0 to …
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