We construct orthonormal bases compatible with bi-variate homogeneous $$\alpha $$ -modulation spaces and the associated of Triebel–Lizorkin type. The construction is based on generating a separable -covering using carefully selected tensor products univariate brushlet functions regard to this covering. show that systems form an unconditional for -spaces

Motivated by their utility in coding of digital communication signals, numerous examples of orthonor-mal wavelet sets that are generated from a bandlim-ited mother wavelet have been constructed. In most of these examples, orthogonality of the replicates at diierent scales is achieved by ensuring that the frequency domain supports at every scale are disjoint. Given the mother wavelet for such a ...

In this paper, non iterative algorithms for the identification of (multivariable) Hammerstein and Wiener systems are presented. The proposed algorithms are numerically robust, since they are based only on least squares estimation and singular value decomposition. For the Hammerstein model, the algorithm provides consistent estimates even in the presence of coloured output noise, under weak assu...

We compare several properties and constructions of the Carlitz polynomials and digit derivatives for continuous functions on Fq[[T ]]. In particular, we show a close relation between them as orthonormal bases. Moreover, parallel to Carlitz’s coefficient formula, we give the closed formula for the expansion coefficients in terms of the digit derivatives.

It is proved that there exist subspaces of bipartite tensor product spaces that have no orthonormal bases that can be perfectly distinguished by means of LOCC protocols. A corollary of this fact is that there exist quantum channels having sub-optimal classical capacity even when the receiver may communicate classically with a third party that represents the channel’s environment.

It is shown that generically, in Baire’s sense, the bound states of Hamiltonian hydrogen atom have spectral measures with exact 0-lower and 1/3-upper generalized fractal dimensions; relation to (a weak form of) dynamical delocalization along orthonormal bases also discussed. Such result a consequence certain distributions eigenvalues for which particular case.

This paper presents a new robust algorithm for the identification of linear time-invariant systems in the frequency domain. The method is computationally very efficient, and accurately synthesises transfer functions which require a large amount of poles. Some numerical difficulties are avoided by combining the use of a Sanathanan-Koerner iteration and orthonormal rational functions.

It is proved that there exist subspaces of bipartite tensor product spaces that have no orthonormal bases that can be perfectly distinguished by means of local operations and classical communication. A corollary of this fact is that there exist quantum channels having suboptimal classical capacity even when the receiver may communicate classically with a third party that represents the channel'...

Spectral representations of the dilation and translation operators on L 2 (R) are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions defined on the functional spectral spaces. The approach is useful for computational purposes.

We develop and analyze a best basis algorithm for orthonormal bases of local cosines which satisfy a uniform bound on their time-frequency concentration. All waveforms are obtained from three elementary window functions by shifts, rescaling, and modulation. For a discrete signal of length N, the complexity is of order N(logN) 2 .