coiflet

Coiflet is a family of orthogonal, compactly supported wavelets designed to have a high number of vanishing moments for both the wavelet and the scaling function. Parameterized by an integer N ≥ 1, the Coiflet-N family achieves N vanishing moments in the wavelet and N+1 vanishing moments in the associated scaling function, providing good polynomial approximation while preserving time localization. The filters used to form the Coiflet wavelets are finite impulse response and are constructed to satisfy orthogonality and smoothness requirements; the resulting wavelets are nearly symmetric, which reduces phase distortion in signal processing.

Coiflets are commonly used in multiresolution analysis, including denoising, compression, and feature extraction for one-dimensional signals and images. They offer a trade-off between the length of the filter, the degree of smoothness, and symmetry, typically requiring longer filters than some Daubechies wavelets but delivering improved symmetry and higher vanishing moments.

In practice, numerical implementations deploy a discrete wavelet transform with Coiflet filters of various orders (for example Coiflet 1, Coiflet 2, etc.), allowing multilevel decomposition and reconstruction. Software libraries for signal processing and data analysis provide Coiflet options alongside other wavelet families such as Daubechies and Symlets.

See also: Wavelet transform, Daubechies wavelets, Symlets, Meyer wavelets.