This is part of a program devoted to the study of wavelets by making use of their Fourier transforms. We shall rst give a constructive characterization of all minimally-supported-frequencies(m.s.f.) wavelets. Then we use this to construct new m.s.f. wavelets, including ones that are not band-limited. We shall also provide a simple necessary and suucient condition for an m.s.f. wavelet to be ass...

1.1 Pictures of complex wavelets Figure 1 shows the six distinct Daubechies’ wavelets with five vanishing moments. Panels (c) and (f) show respectively the familiar extremal phase and least asymmetric real wavelets, while the other panels show the four distinct complex-valued wavelets. Even though these cDws share the same number of vanishing moments, they are visually very different to each ot...

The wavelet dimension function for arbitrary real dilations is defined and used to address several questions involving the existence of MRA wavelets and well-localized wavelets for irrational dilations. The theory of quasi-affine frames for rational dilations and the existence of non-MSF wavelets for certain irrational dilations play an important role in this development. Expansive dilations ad...

Mirror Theory is a syntactic framework developed in (Brody, 1997), where it is offered as a consequence of eliminating purported redundancies in Chomsky’s minimalism (Chomsky, 1995). A fundamental feature of Mirror Theory is its requirement that the syntactic head-complement relation mirror certain morphological relations (such as constituency). This requirement constrains the types of syntacti...

The pulse shape deformation of 80 ps Gaussian input transmitted through a Fabry-P6rot has been determined experimentally and theoretically as a function of the mirror spacing. The effect of mirror surface imperfections is discussed and it is shown that for not too large imperfections there is a strong influence on the transmitted pulse energy whereas the transmitted pulse shape remains almost u...

We describe a method to construct a hierarchical representation of a given implicitly defined algebraic spline curve with the help of weighted spline wavelets. These wavelets are adapted to the region of interest, in our case to the region along the curve, by means of a weighted inner product. The application of two different types of weighted spline wavelets is considered and compared with sta...