Output Filter Aware Optimization of the Noise Shaping Properties of {\Delta}{\Sigma} Modulators via Semi-Definite Programming

The Noise Transfer Function (NTF) of {\Delta}{\Sigma} modulators is typically designed after the features of the input signal. We suggest that in many applications, and notably those involving D/D and D/A conversion or actuation, the NTF should instead be shaped after the properties of the output/reconstruction filter. To this aim, we propose a framework for optimal design based on the Kalman-Yakubovich-Popov (KYP) lemma and semi-definite programming. Some examples illustrate how in practical cases the proposed strategy can outperform more standard approaches.Comment: 14 pages, 18 figures, journal. Code accompanying the paper is available at http://pydsm.googlecode.co

Assigning and combining probabilities in single-case studies

There is currently a considerable diversity of quantitative measures available for summarizing the results in single-case studies. Given that the interpretation of some of them is difficult due to the lack of established benchmarks, the current paper proposes an approach for obtaining further numerical evidence on the importance of the results, complementing the substantive criteria, visual analysis, and primary summary measures. This additional evidence consists of obtaining the statistical significance of the outcome when referred to the corresponding sampling distribution. This sampling distribution is formed by the values of the outcomes (expressed as data nonoverlap, R-squared, etc.) in case the intervention is ineffective. The approach proposed here is intended to offer the outcome"s probability of being as extreme when there is no treatment effect without the need for some assumptions that cannot be checked with guarantees. Following this approach, researchers would compare their outcomes to reference values rather than constructing the sampling distributions themselves. The integration of single-case studies is problematic, when different metrics are used across primary studies and not all raw data are available. Via the approach for assigning p values it is possible to combine the results of similar studies regardless of the primary effect size indicator. The alternatives for combining probabilities are discussed in the context of single-case studies pointing out two potentially useful methods- one based on a weighted average and the other on the binomial test

Synthesis of electrical and mechanical networks of restricted complexity

This dissertation is concerned with the synthesis of linear passive electrical and mechanical networks. The main objective is to gain a better understanding of minimal realisations within the simplest non-trivial class of networks of restricted complexity--the networks of the so-called "Ladenheim catalogue"--and thence establish more general results in the field of passive network synthesis. Practical motivation for this work stems from the recent invention of the inerter mechanical device, which completes the analogy between electrical and mechanical networks. A full derivation of the Ladenheim catalogue is first presented, i.e. the set of all electrical networks with at most two energy storage elements (inductors or capacitors) and at most three resistors. Formal classification tools are introduced, which greatly simplify the task of analysing the networks in the catalogue and help make the procedure as systematic as possible. Realisability conditions are thus derived for all the networks in the catalogue, i.e. a rigorous characterisation of the behaviours which are physically realisable by such networks. This allows the structure within the catalogue to be revealed and a number of outstanding questions to be settled, e.g. regarding the network equivalences which exist within the catalogue. A new definition of "generic" network is introduced, that is a network which fully exploits the degrees of freedom offered by the number of elements in the network itself. It is then formally proven that all the networks in the Ladenheim catalogue are generic, and that they form the complete set of generic electrical networks with at most two energy storage elements. Finally, a necessary and sufficient condition is provided to efficiently test the genericity of any given network, and it is further shown that any positive-real function can be realised by a generic network.The MathWorks Studentship in Engineerin

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature