An introduction to wavelets

Wavelets are mathematical functions that cut up data into di♂erent 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 ♀elds of mathematics,quantum physics, electrical engineering, and seismic geology. Interchanges between these ♀eldsduring 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 ♀eld. I describe the history of wavelets beginning with Fourier, compare wavelet transforms with Fourier transforms, state propertiesand other special aspects of wavelets, and ♀nish with some interesting applications such as image compression, musical tones, and denoising noisy data.