| In this paper a method for parameterizing orthogonal wavelet transforms is presented. The parameter space is given by the rotation angles of the orthogonal 22{ rotations used in the lattice lters realizing the stages of the wavelet transform. Diierent properties of orthogonal wave-let transforms can be expressed in this parameter space. Then, the parameter space is restricted to the set of ro...

Classical spectral analysis in statistics considers decomposition of stationary time series into sinusoidal components. The autocovariance and the spectrum are fundamental elements for analyzing a given time series both in time and frequency domain. However, in practice one frequently observes nonstationary time series. In order to apply spectral analysis to these processes, an extension of the...

Wavelets are the building blocks of wavelet transformations the same way that the functions einx are the building blocks of the ordinary Fourier transformation. But in contrast to sines and cosines, wavelets can be (or almost can be) supported on an arbitrarily small closed interval. This makes wavelets a very powerful tool in dealing with phenomena which change rapidly in time. Statistical wav...

A new progressive transmission scheme using spline biorthogonal wavelet bases is proposed in this paper. First, several wavelet bases are compared with the spline biorthogo-nal wavelet bases. By exploiting the properties of this set of wavelet bases, a fast algorithm involving only additions and subtractions is developed. Due to the multiresolutional nature of the wavelet transform, this scheme...

Tensor product real-valued wavelets have been employed in many applications such as image processing with impressive performance. Though edge singularities are ubiquitous and play a fundamental role in image processing and many other two-dimensional problems, tensor product real-valued wavelets are known to be only sub-optimal since they can only capture edges well along the coordinate axis dir...

The design and analysis of nearly-orthogonal symmetric wavelet filter banks has been studied. Methods for analyzing the correlation of the nearly-orthogonal filter banks are proposed. The basic idea is to impose multiple zeros at the aliasing frequency to a symmetric filter, minimize the deviation of the filter satisfying the orthogonal condition, and a nearly orthogonal filter bank can be obta...

The subject of “wavelets” is expanding at such a tremendous rate that it is impossible to give, within these few pages, a complete introduction to all aspects of its theory. We hope, however, to allow the reader to become sufficiently acquainted with the subject to understand, in part, the enthusiasm of its proponents toward its potential application to various numerical problems. Furthermore, ...