coiflets

Coiflets are a family of orthogonal, compactly supported wavelets developed by Ronald Coifman and Ingrid Daubechies in 1990. They are designed to have a substantial number of vanishing moments for both the scaling function and the wavelet, which makes them effective at representing smooth signals and polynomial trends while enabling sparse representations of more complex components. The resulting filters are finite impulse responses, yielding a discrete wavelet transform that is orthogonal and supports exact reconstruction with fast algorithms.

Coiflets are part of the Daubechies family but incorporate additional moment constraints to improve regularity and symmetry without greatly increasing the support length. They are nearly symmetric, which helps reduce phase distortion in signal processing. Because of their vanishing moments and orthogonality, Coiflets perform well in denoising, compression, feature extraction, and numerical methods such as wavelet-Galerkin approaches to differential equations.

In practice, a Coiflet is selected by order, balancing the number of vanishing moments, regularity, and filter length. Common references and software libraries provide filter coefficients for various Coiflet orders, enabling straightforward implementation in both analysis and applications.