In both applications and wavelet theory, the spline wavelets are especially interesting, in part because of their simple structure. In a previous paper we proved that the function m;l is an m th order spline wavelet having an l th order spline dual wavelet. This enabled us to derive biorthogonal spline wavelet bases. In this paper we rst study the general structure of cardinal spline wavelets, ...

We propose a matrix approach to the computation of BattleLemarié's wavelets. The Fourier transform of the scaling function is the product of the inverse F(x) of a square root of a positive trigonometric polynomial and the Fourier transform of a B-spline of order m . The polynomial is the symbol of a bi-infinite matrix B associated with a B-spline of order 2m . We approximate this bi-infinite ma...

Battle-Lemari e's wavelet has a nice generalization in the bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the lters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass lter when the degree of the bivariate box spline functions increases to 1. The passing and stopping bands of the ideal lter are dependent ...

We give a formula for the duals of the masks associated with trivariate box spline functions. We show how to construct trivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions. The biorthogonal wavelets may have arbitrarily high regularities.

Battle-Lemari e's wavelet has a nice generalization in the bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the lters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass lter when the degree of the bivariate box spline functions increases to 1. The passing and stopping bands of the ideal lter are dependent ...

In 1992 Unser and colleagues proved that the sequence of normalized and scaled B-splines Bm tends to the Gaussian function as the order m increases, [1]. In this article the result of Unser et al. is extended to the derivatives of the B-splines. As a consequence, a certain sequence of wavelets defined by B-splines, tends to the famous Mexican hat wavelet. Another consequence can be observed in ...