Biorthogonal system

About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.

RF simplex spread spectrum receiver and method

Abstract: A method and system are provided for the reception of a biorthogonally-modulated RF signal in a simplex free-space system. The method is found to substantially diminish the coupling between the error probabilities of those bits associated with signal selection and those bits associated with signal polarity in prior art biorthogonal receivers. By decoupling the error probabilities, the polarity information error rate is reduced and consequently the overall error rate of the receiver system is improved. The receiver system preserves soft-decision reliability information for the signal selection bits in a manner so that the information is insensitive to uncompensated amplitude fluctuations in the received signal. The method and system are applicable to all known biorthogonal signal sets but requires a specific interleaving structure in the corresponding transmitter system.

Image Denoising Using Matched Biorthogonal Wavelets

Abstract: Current denoising techniques use the classical ortho normal wavelets for decomposition of an image corrupted with additive white Gaussian noise, upon which various thresholding strategies are built. The use of available biorthogonal wavelets in image denoising is less common because of their poor performance. In this paper, we present a method to design image-matched biorthogonal wavelet bases and report on their potential for denoising. We have conducted experiments on various image datasets namely Natural, Satellite and Medical with the designed wavelets using two existing thresholding strategies. Test results from comparing the performance of matched and fixed biorthogonal wavelets show an average improvement of 35% in MSE for low SNR values (0 to 18 db) in every dataset. This improvement was also seen in the PSNR and visual comparisons. This points to the importance of matching when using wavelet-based denoising.

Exactly solvable two-dimensional complex model with a real spectrum

Abstract: Using supersymmetric intertwining relations of the second order in derivatives, we construct a two-dimensional quantum model with a complex potential for which all energy levels and the corresponding wave functions are obtained analytically. This model does not admit separation of variables and can be considered a complexified version of the generalized two-dimensional Morse model with an additional sinh −2 term. We prove that the energy spectrum of the model is purely real. To our knowledge, this is a rather rare example of a nontrivial exactly solvable model in two dimensions. We explicitly find the symmetry operator, describe the biorthogonal basis, and demonstrate the pseudo-Hermiticity of the Hamiltonian of the model. The obtained wave functions are simultaneously eigenfunctions of the symmetry operator.

Biorthogonal Laurent polynomials, Toeplitz determinants, minimal Toda orbits and isomonodromic tau functions

Abstract: 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 polynomials on the unit circle and tie together the theory of Toda, relativistic Toda, Ablowitz-Ladik and Volterra lattices. We establish corresponding Christoffel-Darboux formulae . For all these classes of polynomials a 2x2 system of Differential-Difference-Deformation equations is analyzed in the most general setting of pseudo measures with arbitrary rational logarithmic derivative. They provide particular classes of isomonodromic deformations of rational connections on the Riemann sphere. The corresponding isomonodromic tau function is explicitly related to the shifted Toeplitz determinants of the moments of the pseudo-measure. In particular the results imply that any (shifted) Toeplitz (Hankel) determinant of a symbol (measure) with arbitrary rational logarithmic derivative is an isomonodromic tau function.