Approximation of L\"owdin Orthogonalization to a Spectrally Efficient Orthogonal Overlapping PPM Design for UWB Impulse Radio

In this paper we consider the design of spectrally efficient time-limited pulses for ultrawideband (UWB) systems using an overlapping pulse position modulation scheme. For this we investigate an orthogonalization method, which was developed in 1950 by Per-Olov L\"owdin. Our objective is to obtain a set of N orthogonal (L\"owdin) pulses, which remain time-limited and spectrally efficient for UWB systems, from a set of N equidistant translates of a time-limited optimal spectral designed UWB pulse. We derive an approximate L\"owdin orthogonalization (ALO) by using circulant approximations for the Gram matrix to obtain a practical filter implementation. We show that the centered ALO and L\"owdin pulses converge pointwise to the same Nyquist pulse as N tends to infinity. The set of translates of the Nyquist pulse forms an orthonormal basis or the shift-invariant space generated by the initial spectral optimal pulse. The ALO transform provides a closed-form approximation of the L\"owdin transform, which can be implemented in an analog fashion without the need of analog to digital conversions. Furthermore, we investigate the interplay between the optimization and the orthogonalization procedure by using methods from the theory of shift-invariant spaces. Finally we develop a connection between our results and wavelet and frame theory.Comment: 33 pages, 11 figures. Accepted for publication 9 Sep 201

Recovery of Missing Samples in Oversampling Formulas for Band Limited Functions

In a previous paper, the author constructed frames and oversampling formulas for band-limited functions, in the framework of the theory of shift-invariant spaces. In this article we study the problem of recovering missing samples. We find a sufficient condition for the recovery of a finite set of missing samples. The condition is expressed as a linear independence of the components of a vector W over the space of trigonometric polynomials determined by the frequencies of the missing samples. We apply the theory to the derivative sampling of any order and we illustrate our results with a numerical experiment.Comment: 19 pages, 3 figures, corrected a few typo

Pluto: A Monte Carlo Simulation Tool for Hadronic Physics

Pluto is a Monte-Carlo event generator designed for hadronic interactions from Pion production threshold to intermediate energies of a few GeV per nucleon, as well as for studies of heavy ion reactions. This report gives an overview of the design of the package, the included models and the user interface.Comment: XI International Workshop on Advanced Computing and Analysis Techniques in Physics Research, April 23-27 2007, Amsterdam, the Netherland

Pluto: a Monte Carlo simulation tool for hadronic physics

Pluto is a Monte-Carlo event generator designed for hadronic interactions from Pion production threshold to intermediate energies of a few GeV per nucleon, as well as for studies of heavy ion reactions. The package is entirely based on ROOT, without the need of additional packages, and uses the embedded C++ interpreter of ROOT to control the event production. The generation of events based on a single reaction chain and the storage of the resulting particle objects can be done with a few lines of a ROOT-macro. However, the complete control of the package can be taken over by the steering macro and user-defined models may be added without a recompilation of the framework. Multi-reaction cocktails can be facilitated as well using either mass-dependent or user-defined static branching ratios. The included physics uses resonance production with mass-dependent Breit-Wigner sampling. The calculation of partial and total widths for resonances producing unstable particles is performed recursively in a coupled-channel approach. Here, particular attention is paid to the electromagnetic decays, motivated by the physics program of HADES. The thermal model supports 2-component thermal distributions, longitudinal broadening, radial blast, direct and elliptic flow, and impact-parameter sampled multiplicities. The interface allows angular distribution models (e.g. for the primary meson emission) to be attached by the user as well as descriptions of multi-particle correlations using decay chain templates. The exchange of mass sampling or momentum generation models is also possible. The first feature allows for consistent coupled-channel calculations, needed for a correct description of hadronic interactions. For elementary reactions, angular distribution models for selected channels are already part of the framework, based on parameterizations of existing data. This report gives an overview of the design of the package, the included models and the user interface

Sub-Nyquist Sampling: Bridging Theory and Practice

Sampling theory encompasses all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark in the development of digital signal processing. In modern applications, an increasingly number of functions is being pushed forward to sophisticated software algorithms, leaving only those delicate finely-tuned tasks for the circuit level. In this paper, we review sampling strategies which target reduction of the ADC rate below Nyquist. Our survey covers classic works from the early 50's of the previous century through recent publications from the past several years. The prime focus is bridging theory and practice, that is to pinpoint the potential of sub-Nyquist strategies to emerge from the math to the hardware. In that spirit, we integrate contemporary theoretical viewpoints, which study signal modeling in a union of subspaces, together with a taste of practical aspects, namely how the avant-garde modalities boil down to concrete signal processing systems. Our hope is that this presentation style will attract the interest of both researchers and engineers in the hope of promoting the sub-Nyquist premise into practical applications, and encouraging further research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin

Event Generators for WW Physics

The report summarizes the results of the activities of the Working Group on Event Generators for WW Physics at CERN during 1995.Comment: 99 Latex, including 30 figures, 24 tables. The report is part of: G.Altarelli,T.Sjostrand and F.Zwirner (eds), Physics at LEP2 CERN 96-0