An oversampled discrete-time Gabor transform (DTGT) has inherent redundancy for signal representation in the joint time-frequency domain. In the proposed multiple-access communication system, this redundancy is used to separate different signals. The DTGTs of all users' signals are transmitted in the same time slots and frequency bands. The DTGTs of the signals can be separated if the analysis ...

We recall the notion of cuspform for Γ = SL2(Z) acting on the upper half-plane, and prove that the orthogonal complement in L(Γ\H) to cuspforms is spanned by pseudo-Eisenstein series, which in turn are expressible as wave packets of Eisenstein series Es. Further we have a Plancherel theorem for this space. The non-trivial harmonic analysis resides in the application of the Fourier transform on ...

We consider the class of biorthogonal polynomials that are used to solve the inverse spectral problem associated to elementary co-adjoint orbits of the Borel group of upper triangular matrices; these orbits are the phase space of generalized integrable lattices of Toda type. Such polynomials naturally interpolate between the theory of orthogonal polynomials on the line and orthogonal polynomial...

In this paper we propose a transmission concept that improves the performance of high rate non-orthogonal space-time block codes. Orthogonal space-time codes have well known rate limitations [9], [7]. If the symbol rate is increased beyond those limits either code orthogonality [5] or the effective diversity gain is necessarily compromised. In the presence of channel coding the performance of n...

1. Preliminaries Theorem A-1. (Theorem 3.1, (Chang, 2012)) Let A ∈ Rm×n be of full column rank with QR factorization A = QR, ∆A be a perturbation in A, and A + ∆A = (Q + ∆Q)(R + ∆R) be the QR-factorization of A + ∆A. Let PA and PA⊥ be the orthogonal projectors onto the range of A and the orthogonal complement of the range of A, respectively. LetQ⊥ be an orthonormal matrix such that matrix [Q,Q⊥...

We review a new theory of orthogonal separation variables on pseudo-Riemannian spaces constant zero curvature via concircular tensors and warped products. then apply this to three-dimensional Minkowski space, obtaining an invariant classification the forty-five separable webs modulo action isometry group. The eighty-eight inequivalent coordinate charts adapted are also determined listed. find n...

Commutator properties are established for periodic smoothest splines (on uniform meshes) operated on by certain pseudo-diierential operators. The commutation involves the operations of multiplication by a smooth function, and application of the operator of orthogonal projection onto a spline space; or the orthogonal projection is replaced by a discrete version of orthogonal projection obtained ...