**Definition:**A wavelet is a function which (a) maps from the real line to the real line, (b) has an average value of zero, (c) has values very near zero except over a bounded domain, and (d) is used for the purpose, analogous to Fourier analysis. Unlike sine waves, wavelets tend to be irregular, asymmetric, and to have values that die out to zero as one approaches positive and negative infinity.

By decomposing a signal into wavelets one hopes not to lose local features of the signal and information about timing. These contrast with Fourier analysis, which tends to reproduce only repeated features of the original function or series.

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