New sampling theorem and multiplicative filtering in the FRFT domain

Having in consideration a fractional convolution associated with the fractional Fourier transform (FRFT), we propose a novel reconstruction formula for bandlimited signals in the FRFT domain without using the classical Shannon theorem. This may be considered the main contribution of this work, and numerical experiments are implemented to demonstrate the effectiveness of the proposed sampling theorem. As a second goal, we also look for the designing of multiplicative filters. Indeed, we also convert the multiplicative filtering in FRFT domain to the time domain, which can be realized by Fast Fourier transform. Two concrete examples are included where the use of the present results is illustrated.publishe

Second year technical report on-board processing for future satellite communications systems

Advanced baseband and microwave switching techniques for large domestic communications satellites operating in the 30/20 GHz frequency bands are discussed. The nominal baseband processor throughput is one million packets per second (1.6 Gb/s) from one thousand T1 carrier rate customer premises terminals. A frequency reuse factor of sixteen is assumed by using 16 spot antenna beams with the same 100 MHz bandwidth per beam and a modulation with a one b/s per Hz bandwidth efficiency. Eight of the beams are fixed on major metropolitan areas and eight are scanning beams which periodically cover the remainder of the U.S. under dynamic control. User signals are regenerated (demodulated/remodulated) and message packages are reformatted on board. Frequency division multiple access and time division multiplex are employed on the uplinks and downlinks, respectively, for terminals within the coverage area and dwell interval of a scanning beam. Link establishment and packet routing protocols are defined. Also described is a detailed design of a separate 100 x 100 microwave switch capable of handling nonregenerated signals occupying the remaining 2.4 GHz bandwidth with 60 dB of isolation, at an estimated weight and power consumption of approximately 400 kg and 100 W, respectively

High-resolution algorithms for the reconstruction of the equivalent currents of an antenna by means of modal theory and a priori information

El objetivo del diagnóstico de antenas es la detección de errores en antena fabricadas. Dado que este diagnóstico es difícil de realizar simplemente observando medidas de campo, el diagnóstico se realiza usando las corrientes equivalentes reconstruidas en una superficie próxima a la antena. Esta tesis describe las diferentes posibilidades de realizar esta reconstrucción en una superficie plana a partir de medidas esféricas en campo próximo. En concreto, se estudian extensivamente, y se aplican a situaciones reales, las técnicas de la expansión modal. El problema principal de las técnicas modales es la limitación en la resolución de las corrientes equivalentes. La razón de esta limitación es la pequeña región disponible del espectro de ondas planas (cuya transformada de Fourier son las corrientes equivalentes). En esta tesis se estudia este problema, se muestran varios ejemplos y se describen las posibilidades de mejorar la resolución. De entre estas posibilidades, se propone el uso de una técnica de extrapolación con la que estimar el espectro no visible a partir de la región conocida (el espectro visible) y de información adicional sobre la antena como, por ejemplo, el tamaño de la antena. Entre las diferentes técnicas de extrapolación, se describen y comparan las técnicas más usadas comúnmente. En primer lugar, se aplica el algoritmo iterativo de Papoulis-Gerchberg usando el tamaño y la forma de la antena. Después se describen las versiones directas de este algoritmo, es decir la matriz de extrapolación por filas y columnas y la matriz de extrapolación generalizada. Finalmente, se estudia la transformación PDFT y se compara con los algoritmos anteriores. Todas estas técnicas son aplicadas en situaciones reales con una importante mejora en la resolución. El último capítulo de esta tesis trata de los procedimientos de calibración de sonda. Estos procedimientos son especialmente importantes en el diagnóstico de antenas.Sánchez Escuderos, D. (2009). High-resolution algorithms for the reconstruction of the equivalent currents of an antenna by means of modal theory and a priori information [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8323Palanci

Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective

Bibliography: p. 208-225.Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature. The most significant advantages claimed are high reconstruction quality at low coding rates, rapid decoding, and "resolution independence" in the sense that an encoded image may be decoded at a higher resolution than the original. While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation. . So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant. Although the conditions imposed on these transforms may be shown to be sufficient to guarantee that an approximation of the original image can be reconstructed, there is no obvious theoretical reason to expect this to represent an efficient representation for image coding purposes. The usual analogy with vector quantisation, in which each image is considered to be represented in terms of code vectors extracted from the image itself is instructive, but transforms the fundamental problem into one of understanding why this construction results in an efficient codebook. The signal property required for such a codebook to be effective, termed "self-affinity", is poorly understood. A stochastic signal model based examination of this property is the primary contribution of this dissertation. The most significant findings (subject to some important restrictions} are that "self-affinity" is not a natural consequence of common statistical assumptions but requires particular conditions which are inadequately characterised by second order statistics, and that "natural" images are only marginally "self-affine", to the extent that fractal image compression is effective, but not more so than comparable standard vector quantisation techniques

Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior

Digital Signal Processing (Second Edition)

This book provides an account of the mathematical background, computational methods and software engineering associated with digital signal processing. The aim has been to provide the reader with the mathematical methods required for signal analysis which are then used to develop models and algorithms for processing digital signals and finally to encourage the reader to design software solutions for Digital Signal Processing (DSP). In this way, the reader is invited to develop a small DSP library that can then be expanded further with a focus on his/her research interests and applications. There are of course many excellent books and software systems available on this subject area. However, in many of these publications, the relationship between the mathematical methods associated with signal analysis and the software available for processing data is not always clear. Either the publications concentrate on mathematical aspects that are not focused on practical programming solutions or elaborate on the software development of solutions in terms of working ‘black-boxes’ without covering the mathematical background and analysis associated with the design of these software solutions. Thus, this book has been written with the aim of giving the reader a technical overview of the mathematics and software associated with the ‘art’ of developing numerical algorithms and designing software solutions for DSP, all of which is built on firm mathematical foundations. For this reason, the work is, by necessity, rather lengthy and covers a wide range of subjects compounded in four principal parts. Part I provides the mathematical background for the analysis of signals, Part II considers the computational techniques (principally those associated with linear algebra and the linear eigenvalue problem) required for array processing and associated analysis (error analysis for example). Part III introduces the reader to the essential elements of software engineering using the C programming language, tailored to those features that are used for developing C functions or modules for building a DSP library. The material associated with parts I, II and III is then used to build up a DSP system by defining a number of ‘problems’ and then addressing the solutions in terms of presenting an appropriate mathematical model, undertaking the necessary analysis, developing an appropriate algorithm and then coding the solution in C. This material forms the basis for part IV of this work. In most chapters, a series of tutorial problems is given for the reader to attempt with answers provided in Appendix A. These problems include theoretical, computational and programming exercises. Part II of this work is relatively long and arguably contains too much material on the computational methods for linear algebra. However, this material and the complementary material on vector and matrix norms forms the computational basis for many methods of digital signal processing. Moreover, this important and widely researched subject area forms the foundations, not only of digital signal processing and control engineering for example, but also of numerical analysis in general. The material presented in this book is based on the lecture notes and supplementary material developed by the author for an advanced Masters course ‘Digital Signal Processing’ which was first established at Cranfield University, Bedford in 1990 and modified when the author moved to De Montfort University, Leicester in 1994. The programmes are still operating at these universities and the material has been used by some 700++ graduates since its establishment and development in the early 1990s. The material was enhanced and developed further when the author moved to the Department of Electronic and Electrical Engineering at Loughborough University in 2003 and now forms part of the Department’s post-graduate programmes in Communication Systems Engineering. The original Masters programme included a taught component covering a period of six months based on two semesters, each Semester being composed of four modules. The material in this work covers the first Semester and its four parts reflect the four modules delivered. The material delivered in the second Semester is published as a companion volume to this work entitled Digital Image Processing, Horwood Publishing, 2005 which covers the mathematical modelling of imaging systems and the techniques that have been developed to process and analyse the data such systems provide. Since the publication of the first edition of this work in 2003, a number of minor changes and some additions have been made. The material on programming and software engineering in Chapters 11 and 12 has been extended. This includes some additions and further solved and supplementary questions which are included throughout the text. Nevertheless, it is worth pointing out, that while every effort has been made by the author and publisher to provide a work that is error free, it is inevitable that typing errors and various ‘bugs’ will occur. If so, and in particular, if the reader starts to suffer from a lack of comprehension over certain aspects of the material (due to errors or otherwise) then he/she should not assume that there is something wrong with themselves, but with the author