Wavelet

Summary

A wavelet is a function $\psi$ on $\R$ whose dilations by powers of $2$ and integer translations form an orthonormal basis of $L^2(\R)$. Each basis function is localized near a position and at a scale, so a wavelet expansion describes a function at all levels of detail. In a wider sense, any oscillating function with integral zero that is used in a continuous wavelet transform is called a wavelet. Wavelets are used in signal and image compression, numerical analysis and harmonic analysis.