Biorthogonal system

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

Optimization Design of Biorthogonal Wavelets for Embedded Image Coding

Abstract: We present here a simple technique for parametrization of popular biorthogonal wavelet filter banks (BWFBs) having vanishing moments (VMs) of arbitrary multiplicity. Given a prime wavelet filter with VMs of arbitrary multiplicity, after formulating it as a trigonometric polynomial depending on two free parameters, we prove the existence of its dual filter based on the theory of Diophantine equation. The dual filter permits perfect reconstruction (PR) and also has VMs of arbitrary multiplicity. We then give the complete construction of two-parameter families of 17/11 and 10/18 BWFBs, from which any linear-phase 17/11 and 10/18 BWFB possessing desired features could be derived with ease by adjusting the free parameters. In particular, two previously unpublished BWFBs for embedded image coding are constructed, both have optimum coding gains and rational coefficients. Extensive experiments show that our new BWFBs exhibit performance equal to Winger's W--17/11 and Villasenor's V--10/18 (superior to CDF--9/7 by Cohen et al. and Villasenor's V--6/10) for image compression, and yet require slightly lower computational costs.

An optimal circular 16-QAM modulation technique for wavelet and fourier based OFDM

Abstract: A new approach of an optimal 16-QAM modulation has been introduced to be used for both Fourier and wavelet based OFDM. The comparison between circular and square 16-QAM is included. It is shown that the power consumption of circular is better than the square by 0.5359 W or −2.71 dB for the same minimum distance 2d. Simulation works for Fourier and wavelet based OFDM have been performed. In Fourier base OFDM, the circular has slightly out-performed the square when the number of subcarriers is varied from 32 to 256 at different BER values. When considering wavelet based OFDM, all wavelet families except Biorthogonal and Reverse-Biorthogonal have performed similar result for both modulation schemes. Of all Biorthogonal families, bior5.5 is the most out-performed one when using circular and square 16-QAM respectively.

Normalized trigonometric splines of Lagrange type

Abstract: Bϕ-splines, which are a nonpolynomial generalization of the well-known B-splines, are investigated. Bϕ-splines arise from approximation relations regarded as a system of linear algebraical equations, from which both polynomial and nonpolynomial splines are derived. Third-order normalized trigonometric splines of Lagrange type (zero height) determined by the generating vector function ϕ(t) = (1, sin t, cos t, sin2 t)T are constructed. These splines are twice continuously differentiable and have minimal compact support. A system of functionals biorthogonal to Bϕ-splines is defined. The solution of the interpolation problem generated by the resulting biorthogonal system in the space of Bϕ-splines is found.

Organization of optimal nonuniform lapped biorthogonal transforms based on coding efficiency

Abstract: In this paper, we present optimal nonuniform lapped biorthogonal transforms for image compression. Subband coding using wavelet transforms have received a lot of attention because of multiresolution representation. The wavelet transform is regarded as a nonuniform filter bank and is constructed using the tree structure of a two-channel filter bank. However, it may not be optimal in the sense of energy compaction. If we can design nonuniform filter banks directly, it is possible to overcome the conventional wavelet transform. We then design a direct-structured nonuniform filter bank with a lapping window, called NULBT. Finally we show some examples and confirm the validity of our method.

Initial value problem with non‐Hermitian radial mode equations

Abstract: A biorthogonal set of expansion functions is introduced for the radial mode problem that occurs for drift waves and trapped particle modes in nonuniform plasmas. With a vector space representation of the eigenfunctions concise time dependent and time independent perturbation theory formulae are obtained for the system.