β Scribed by Graps A.
No coin nor oath required. For personal study only.
Wavelets are mathematical functions that cut up data into diβerent frequency components, and then study each component with a resolution matched to its scale. They have advantages over traditional Fourier methods in analyzing physical situations where the signal containsdiscontinuities and sharp spikes. Wavelets were developed independently in the βelds of mathematics,quantum physics, electrical engineering, and seismic geology. Interchanges between these βeldsduring the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, and earthquake prediction. This paper introduces wavelets to the interested technical person outside of the digital signal processing βeld. I describe the history of wavelets beginning with Fourier, compare wavelet transforms with Fourier transforms, state propertiesand other special aspects of wavelets, and βnish with some interesting applications such as image compression, musical tones, and denoising noisy data.
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