Key Words: Wavelets, Filter Banks, Hilbert-Space Filling Curve,

Wavelet theory emerged as a powerful tool for providing localized time-frequency expansion for signal At the same time, another field, filter banks, is firmly established as one of the most efficient methods for compressing signal ranging from speech to images. These two fields are closely related. Filter banks can be viewed as a ‘‘Discrete Wavelet Transform’’. This conceptual idea is used in our research to develop two-dimensional wavelets.

One approach to (2D) wavelet modeling is to extend one-dimensional (1D) Wavelet to a separable (2D) Wavelet; however, this approach disregards any spatial orientation. More recent effort have been concentrated on a ‘‘true’’, non-trivial (2D) Wavelet, which means sampling and filtering are not separable, both from the filter bank and the Wavelets aspects.

Although this true (2D) Wavelet modeling approach suffers from some drawbacks (e.g. higher computational complexity), it offers important advantages (e.g. better filter and a better orientation selectivity). Earlier nonseparable (2D) Wavelet research often used polyphase components which results in filters with parallelepiped shape passband support; yet, in some sense, it is still separable dua to the separability property of polyphase networks.

In this paper, we develop nonseparable filters and sampling, as a step toward the design of ‘‘true’’ (2D) Discrete Wavelet, using a special sacanning path, based on the space filling curve, the Hilbert Peano Curve, instead of a rastar scanning, to represent a (2D) system.

If this scanning is orderly, symmetric and hierarchical fractal shows self-similarity with respect to scales as scanning density increases, and preserve orientation at all scales, thus the nonseparable filters are sutable to be synthesized by filter response at various orientations (the basis filters). In other words we intent to find filter response3 at various orientations that could synthesize a nonseparable filter

We use Tensorial Product for the best bases of the Wavelet approach.