Wavelets and filter banks: theory and design

Wavelets and filter banks: theory and design

Wavelets, filter banks and multiresolution signal analysis, have been used independently in the fields of applied mathematics, computer vision and signal processing. It is interesting to note that they performed similar functions in different fields. It is recently, that they converged to form a single theory. In the paper, it is shown that the fundamental idea was the same in all the fields i....

Wavelets And Filter Banks

Wavelet and short-time Fourier analysis is introduced in the context of frequency decompo-sitions. Wavelet type frequency decompositions are associated with lter banks, and using thisfact, lter bank theory is used to construct multiplicity M wavelet frames and tight frames. Theway in which lter banks lead to decomposition and recomposition of arbitrary separable Hilbertspaces is...

Orthogonal complex filter banks and wavelets: some properties and design

Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases offer a number of potential advantageous properties. For example, it has been recently suggested that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property, then it must exhibit linear phase as well. In th...

The theory and design of arbitrary-length cosine-modulated filter banks and wavelets, satisfying perfect reconstruction

Vector-valued wavelets and vector filter banks

In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector lter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued ...