In this paper, we obtain symmetric C∞ real-valued tight wavelet frames in L2(R) with compact support and the spectral frame approximation order. Furthermore, we present a family of symmetric compactly supported C∞ orthonormal complex wavelets in L2(R). A complete analysis of nonstationary tight wavelet frames and orthonormal wavelet bases in L2(R) is given.

A provably stable reduced order model, based on a projection onto a scaled orthonormal Laguerre basis, followed by a SVD step, is proposed. The method relies on the conformal mapping properties induced by the complete orthonormal scaled Laguerre basis, allowing a mapping from the discrete-stable case to the continuous-stable case and vice versa.

A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform on the real line is proved. To this end we state, in terms of Bessel functions, an orthonormal system which is complete in L2((−1, 1), |x|2α+1 dx). This orthonormal system is a generalization of the classical exponential system defining Fourier series.

Based on the common Hermite-Gaussian modes, a general class of orthonormal Hermite-Gaussian-type modes is introduced. Such modes can most easily be defined by means of their generating function. It is shown that these modes remain in their class of orthonormal Hermite-Gaussiantype modes, when they propagate through first-order optical systems. A propagation law for the generating function is fo...

we define a new function-valued inner product on l2(g), called ?-bracket product, where g is a locally compact abelian group and ? is a topological isomorphism on g. we investigate the notion of ?-orthogonality, bessel's inequality and ?-orthonormal bases with respect to this inner product on l2(g).

This paper presents a new method for designing two-band orthonormal IIR wavelet "lter banks using allpass "lters. It is well known that orthonormal wavelet bases can be generated by paraunitary "lter banks. Thus, synthesis of orthonormal wavelet bases can be reduced to the design of paraunitary "lter banks. In this paper, two-band orthonormal IIR wavelet "lter banks using a parallel connection ...