Classification of Nonexpansive Symmetric Extension Transforms for Multirate Filter Banks

This paper describes and classifies a family of invertible discrete-time signal transforms, referred to assymmetric extension transforms(SET's), for finite-length signals. SET's are algorithms for applying perfect reconstruction multirate filter banks to symmetric extensions of finite-length signals, thereby avoiding the boundary artifacts introduced by simple periodic extension. A key point is when such symmetric decompositions can be formed with no increase in data storage requirements (“nonexpansive decompositions”). Transforms based on three types of symmetric extension and four classes of linear phase filters are analyzed in terms of their memory requirements for generalM-channel perfect reconstruction filter banks. The classification is shown to be complete in the sense that it contains all possible nonexpansive SET's. Completeness is then used to deduce design constraints on the construction of nonexpansiveM-channel SET's, including new obstructions to the existence of certain classes of filter banks. This paper also forms the principal technical reference on the SET algorithms incorporated in the Federal Bureau of Investigation's digital fingerprint image coding standard.     

Approximation by translates of refinable functions

Summary. The functions are refinable if they are combinations of the rescaled and translated functions . This is very common in scientific computing on a regular mesh. The space of approximating functions with meshwidth is a subspace of with meshwidth . These refinable spaces have refinable basis functions. The accuracy of the computations depends on , the order of approximation, which is determined by the degree of polynomials that lie in . Most refinable functions (such as scaling functions in the theory of wavelets) have no simple formulas. The functions are known only through the coefficients in the refinement equation – scalars in the traditional case, matrices for multiwavelets. The scalar "sum rules" that determine are well known. We find the conditions on the matrices that yield approximation of order from . These are equivalent to the Strang–Fix conditions on the Fourier transforms , but for refinable functions they can be explicitly verified from the . Received August 31, 1994 / Revised version received May 2, 1995     

Magnetic exchange interactions in tetrabromocuprate compounds

Magnetic and structural data for 28 compounds containing the tetrabromocuprate ion are presented. The parameters which affect the strength and sign of the magnetic superexchange interaction via non-bonding contacts between bromide ions are described and a system for describing the topology of the interaction between tetrahedra is proposed. Analysis of the data suggests that the primary factors affecting the magnetic exchange are the Br?Br distance, the Cu-Br?Br angle and the Cu-Br?Br-Cu dihedral angle.     

Synthesis, structure, theoretical studies, and Ligand exchange reactions of monomeric, T-shaped arylpalladium(II) halide complexes with an additional, weak agostic interaction

A series of monomeric arylpalladium(II) complexes LPd(Ph)X (L = 1-AdPtBu2, PtBu3, or Ph5FcPtBu2 (Q-phos); X = Br, I, OTf) containing a single phosphine ligand have been prepared. Oxidative addition of aryl bromide or aryl iodide to bis-ligated palladium(0) complexes of bulky, trialkylphosphines or to Pd(dba)2 (dba = dibenzylidene acetone) in the presence of 1 equiv of phosphine produced the corresponding arylpalladium(II) complexes in good yields. In contrast, oxidative addition of phenyl chloride to the bis-ligated palladium(0) complexes did not produce arylpalladium(II) complexes. The oxidative addition of phenyl triflate to PdL2 (L = 1-AdPtBu2, PtBu3, or Q-phos) also did not form arylpalladium(II) complexes. The reaction of silver triflate with (1-AdPtBu2)Pd(Ph)Br furnished the corresponding arylpalladium(II) triflate in good yield. The oxidative addition of phenyl bromide and iodide to Pd(Q-phos)2 was faster than oxidative addition to Pd(1-AdPtBu2)2 or Pd(PtBu3)2. Several of the arylpalladium complexes were characterized by X-ray diffraction. All of the arylpalladium(II) complexes are T-shaped monomers. The phenyl ligand, which has the largest trans influence, is located trans to the open coordination site. The complexes appear to be stabilized by a weak agostic interaction of the metal with a ligand C-H bond positioned at the fourth-coordination site of the palladium center. The strength of the Pd.H bond, as assessed by tools of density functional theory, depended upon the donating properties of the ancillary ligands on palladium.