Topic
Biorthogonal system
About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.
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TL;DR: In this paper, the authors analyzed polynomials Pn that are biorthogonal to dilates of a positive measure μ, supported on (0, ∞): ============∫0∞Pn(x)dμ(σn,jx)=0,1≤j≤n.
5 citations
05 Jun 2000
TL;DR: It is shown that the design of optimal DMT systems can be formulated as a hypothetical design problem of optimal subband coders, and the solution can be obtained using existing design methods for optimal biorthogonal sub band coders.
Abstract: The discrete multitone modulation (DMT) systems have been widely used in various applications. The DMT system can be considered as a dual of a subband coder, obtained by using the synthesis bank as the transmitter and analysis bank as the receiver. In designing optimal subband coders, the objective is to minimize output quantization noise, whereas in the problem of designing optimal DMT system, the objective function to be minimized is the transmitted power. We show that the design of optimal DMT systems can be formulated as a hypothetical design problem of optimal subband coders. The solution of optimal DMT system can be obtained using existing design methods for optimal biorthogonal subband coders.
5 citations
01 Mar 2001
5 citations
05 Sep 2005
TL;DR: This paper studies a BPPM modulated TH-UWB system with RAKE reception over block fading channels and finds the capacity and error rate performance are derived over a multipath fading channel for both the single user and multiple access cases.
Abstract: Ultra-wideband (UWB) transmission is a promising technology for future high speed wireless communications RAKE reception is important since it can make use of the rich multipath of UWB systems to improve system performance and capacity At the same time, much research has been directed towards finding efficient modulation schemes for UWB systems Recently, biorthogonal pulse position modulation (BPPM), which combines pulse position modulation (PPM) and biorthogonal signals has been proposed for UWB systems In this paper we study a BPPM modulated TH-UWB system with RAKE reception over block fading channels The capacity and error rate performance are derived over a multipath fading channel for both the single user and multiple access cases Numerical results are given to illustrate the theoretical results
5 citations
TL;DR: In this paper, a strengthened Cauchy-Schwarz inequality for one-dimensional biorthogonal wavelets is proved for a class of Hilbert spaces defined in terms of weighted Fourier transforms, which contain as relevant examples the standard Sobolev spaces H ( s ) as well as their homogeneous version.
5 citations