Quantization Errors of fGn and fBm Signals

In this Letter, we show that under the assumption of high resolution, the quantization errors of fGn and fBm signals with uniform quantizer can be treated as uncorrelated white noises

Global stability, limit cycles and chaotic behaviors of second order interpolative sigma delta modulators

It is well known that second order lowpass interpolative sigma delta modulators (SDMs) may suffer from instability and limit cycle problems when the magnitudes of the input signals are at large and at intermediate levels, respectively. In order to solve these problems, we propose to replace the second order lowpass interpolative SDMs to a specific class of second order bandpass interpolative SDMs with the natural frequencies of the loop filters very close to zero. The global stability property of this class of second order bandpass interpolative SDMs is characterized and some interesting phenomena are discussed. Besides, conditions for the occurrence of limit cycle and fractal behaviors are also derived, so that these unwanted behaviors will not happen or can be avoided. Moreover, it is found that these bandpass SDMs may exhibit irregular and conical-like chaotic patterns on the phase plane. By utilizing these chaotic behaviors, these bandpass SDMs can achieve higher signal-to-noise ratio (SNR) and tonal suppression than those of the original lowpass SDMs

On Unlimited Sampling

Shannon's sampling theorem provides a link between the continuous and the discrete realms stating that bandlimited signals are uniquely determined by its values on a discrete set. This theorem is realized in practice using so called analog--to--digital converters (ADCs). Unlike Shannon's sampling theorem, the ADCs are limited in dynamic range. Whenever a signal exceeds some preset threshold, the ADC saturates, resulting in aliasing due to clipping. The goal of this paper is to analyze an alternative approach that does not suffer from these problems. Our work is based on recent developments in ADC design, which allow for ADCs that reset rather than to saturate, thus producing modulo samples. An open problem that remains is: Given such modulo samples of a bandlimited function as well as the dynamic range of the ADC, how can the original signal be recovered and what are the sufficient conditions that guarantee perfect recovery? In this paper, we prove such sufficiency conditions and complement them with a stable recovery algorithm. Our results are not limited to certain amplitude ranges, in fact even the same circuit architecture allows for the recovery of arbitrary large amplitudes as long as some estimate of the signal norm is available when recovering. Numerical experiments that corroborate our theory indeed show that it is possible to perfectly recover function that takes values that are orders of magnitude higher than the ADC's threshold.Comment: 11 pages, 4 figures, copy of initial version to appear in Proceedings of 12th International Conference on Sampling Theory and Applications (SampTA

The Hipparcos Transit Data: What, why and how?

The Hipparcos Transit Data are a collection of partially reduced, fully calibrated observations of (mostly) double and multiple stars obtained with the ESA Hipparcos astrometry satellite. The data are publicly available, as part of the CD-ROM set distributed with the Hipparcos and Tycho Catalogues (ESA SP--1200, 1997), for about a third of the Hipparcos Catalogue entries including all confirmed or suspected non-single stars. The Transit Data consist of signal modulation parameters derived from the individual transits of the targets across the Hipparcos focal grid. The Transit Data permit re-reduction of the satellite data for individual objects, using arbitrarily complex object models in which time-variable photometric as well as geometric characteristics may be taken into account. We describe the structure and contents of the Transit Data files and give examples of how the data can be used. Some of the applications use standard astronomical software: Difmap or AIPS for aperture synthesis imaging, and GaussFit for detailed model fitting. Fortran code converting the data into formats suitable for these application programs has been made public in order to encourage and facilitate the use of Hipparcos Transit Data.Comment: A&AS, accepted for publication, 17 pages, 9 figures, 1 Table, Software available via http://www.astro.lu.se/~lennart/TD/index.html, Figures 4, 5, 6 and 7 need to copied separately, A complete postscript file can be found at http://www.astro.lu.se/~lennart/TD/ds1699.ps.g

Theory and applications of delta-sigma analogue-to-digital converters without negative feedback

Analog-to-digital converters play a crucial role in modern audio and communication design. Conventional Nyquist converters are suitable only for medium resolutions and require analog components that are precise and highly immune to noise and interference. In contrast, oversampling converters can achieve high resolutions (>20bits) and can be implemented using straightforward, high-tolerance analog components. In conventional oversampled modulators, negative feedback is applied in order to control the dynamic behavior of a system and to realize the attenuation of the quantization noise in the signal band due to noise shaping. However, feedback can also introduce undesirable effects such as limit cycles, jitter problems in continuous-time topologies, and infinite impulse responses. Additionally, it increases the system complexity due to extra circuit components such as nonlinear multi-bit digital-to-analog converters in the feedback path. Moreover, in certain applications such as wireless, biomedical sensory, or microphone implementations feedback cannot be applied. As a result, the main goal of this thesis is to develop sigma-delta data converters without feedback. Various new delta-sigma analog-to-digital converter topologies are explored their mathematical models are presented. Simulations are carried out to validate these models and to show performance results. Specifically, two topologies, a first-order and a second-order oscillator-based delta-sigma modulator without feedback are described in detail. They both can be implemented utilizing VCOs and standard digital gates, thus requiring only few components. As proof of concept, two digital microphones based on these delta-sigma converters without feedback were implemented and experimental results are given. These results show adequate performance and provide a new approach of measuring