Optimal Bell Functions for Biorthogonal Local Trigonometric Bases

Biorthogonal Smooth Local Trigonometric Bases

In this paper we discuss smooth local trigonometric bases. We present two generalizations of the orthogonal basis of Malvar and Coifman-Meyer: biorthogonal and equal parity bases. These allow natural representations of constant and, sometimes, linear components. We study and compare their approximation properties and applicability in data compression. This is illustrated with numerical examples.

Fast Compression of Seismic Data with Local Trigonometric Bases

Our goal in this paper is to provide a fast numerical implementation of the local trigonometric bases algorithm1 in order to demonstrate that an advantage can be gained by constructing a biorthogonal basis adapted to a target image. Different choices for the bells are proposed, and an extensive evaluation of the algorithm was performed on synthetic and seismic data. Because of its ability to re...

Biorthogonal Local Trigonometric Bases

Detection and Classification of Harmonic Transients by Using Trigonometric Smooth Wavelet-Packets Erkennung und Klassifizierung von harmonischen Transienten mit trigonometrischen glatten Wavelet-Paketen

The proposed contribution describes a method for the detection and classification of harmonic transients, as they occur in electrical networks. The method uses, as bases, a special class of wavelet-packets, i. e. smooth biorthogonal sine and cosine-packets in order to find the best ’’Shannon-basis“. The algorithm is based on the minimization of Shannon‘s function for the decomposed wanted signa...

Biorthogonal bases with local support and approximation properties

We construct locally supported basis functions which are biorthogonal to conforming nodal finite element basis functions of degree p in one dimension. In contrast to earlier approaches, these basis functions have the same support as the nodal finite element basis functions and reproduce the conforming finite element space of degree p − 1. Working with Gauß–Lobatto nodes, we find an interesting ...