# Wavelet

From AMS Glossary

## wavelet

A member of a family of functions generated by taking translations [e.g.,

*w*(*t*) →*w*(*t*+ 1)] and scalings [e.g.,*w*(*t*) →*w*(2*t*)] of a function*w*(*t*), called the "mother" wavelet.The choice of

*w*(*t*) is limited by the condition that the square of*w*(*t*) be integrable over all*t*. Linear combinations of wavelets are used to represent wavelike signals. The wavelet decomposition of a signal offers an advantage over the Fourier decomposition in that local or short-term contributions to the signal can be better represented.