Wavelets are functions, like sines and cosines, that satisfy certain requirements.
These functions may be used as basis functions in the representaion of some arbitrary function, in a manner similar to Fourier analysis which uses sines and cosines as basis functions. For example, functions having sharp spikes or discontinuities will require a large number of fourier basis functions if they are to be accurately represented. In contrast, if a wavelet basis is utilized, significantly fewer terms are required. Wavelets, like sinusoids, integrate to zero, but wavelets are localized in both frequency and time, whereas fourier basis functions are localized only in frequency. This additional localization property of wavelets may be used to the advantage of those who are faced with problems involving large and noisy data sets.