Wavelets are mathematical functions that cut up data into dierent 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 contains
discontinuities and sharp spikes. Wavelets were developed independently in the elds of mathematics,
quantum physics, electrical engineering, and seismic geology. Interchanges between these elds
during 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 properties
and other special aspects of wavelets, and nish with some interesting applications such as image compression, musical tones, and denoising noisy data.