wavelet A basis function, W, that yields the representation of a function f(x) of the form: f(x) = ∑b_jkW(2^jx – k)

Wavelets are based on two fundamental ideas: dilation and translation. The construction of wavelets begins with the solution to a dilation equation: φ(x) = ∑c_kφ(2x – k)

φ(x) is called the scaling function. W can then be derived from φ(x): W(x) = ∑(–1)^kc_1–kφ(2x – k)

Wavelets are particularly useful for representing functions that are local in time and frequency. The idea of wavelets grew out of seismic analysis and is now a rapidly developing area in mathematics. There are elegant recursive algorithms for decomposing a signal into its wavelet coefficients and for reconstructing a signal from its wavelet coefficients.

wave·let / ˈwāvlit/ • n. a small wave of water; a ripple.