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

Inverse Dynamics Problems

The inverse dynamics problem was developed in order to provide researchers with the state of the art in inverse problems for dynamic and vibrational systems. Contrasted with a forward problem, which solves for the system output in a straightforward manner, an inverse problem searches for the system input through a procedure contaminated with errors and uncertainties. An inverse problem, with a focus on structural dynamics, determines the changes made to the system and estimates the inputs, including forces and moments, to the system, utilizing measurements of structural vibration responses only. With its complex mathematical structure and need for more reliable input estimations, the inverse problem is still a fundamental subject of research among mathematicians and engineering scientists. This book contains 11 articles that touch upon various aspects of inverse dynamic problems

Investigation into zero-crossing techniques as a viable means of speech recognition

The idea behind this research is to demonstrate how a fundamental characteristic of speech (zero-crossing information) may be exploited in the development of a low cost, highly effective speech recognition system. The system is to be used to recognise a small vocabulary of isolated speech. Although intended to be speaker dependent, the system is also tested for speaker independence. A brief description of how speech is produced and recognised by a human subject is first presented. Following this, some features of both voiced and unvoiced speech signals and their associated spectra are discussed in relation to zero-crossing information. Phonemes and their segmentation (using zero-crossing data or otherwise) are also examined. A brief discussion of stationarity and its effects on zero-crossings is then given. The choice of pre-processing filters is also mentioned. Two methods of speech recognition implementing zero-crossing information are then discussed. The first technique studied analyses the ‘spacing’ between zero-crossings, producing a signal whose amplitude is proportional to the distance between successive crossings. The possibility of this system, (termed Sinusoidal Instantaneous Frequency Extractor (SIFE) [14]), producing effective recognition parameters is examined. A second analysis technique, called Higher Order Crossing Analysis (HOC) [25], is then introduced. This method extracts higher order zero-crossing information from the signal using various filtering techniques and uses this data to recognise the speech signal. Modified versions of both methods were developed, tested and found to be more effective and adaptable than their predecessors. A new parameter (Columnised Higher Order Crossing (CHOC)) was developed and found to be more effective than HOC. Dynamic Time Warping was then implemented to pattern match CHOC templates with CHOC test signals, enabling a percentage success rate for the CHOC system to be achieved (-90% ). Finally, a comparison of the two systems is then made and a discussion about their effectiveness is given

Investigations on the properties and estimation of earth response operators from EM sounding data

Incl. 3 reprints at backAvailable from British Library Document Supply Centre- DSC:D82993 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

Friction, Vibration and Dynamic Properties of Transmission System under Wear Progression

This reprint focuses on wear and fatigue analysis, the dynamic properties of coating surfaces in transmission systems, and non-destructive condition monitoring for the health management of transmission systems. Transmission systems play a vital role in various types of industrial structure, including wind turbines, vehicles, mining and material-handling equipment, offshore vessels, and aircrafts. Surface wear is an inevitable phenomenon during the service life of transmission systems (such as on gearboxes, bearings, and shafts), and wear propagation can reduce the durability of the contact coating surface. As a result, the performance of the transmission system can degrade significantly, which can cause sudden shutdown of the whole system and lead to unexpected economic loss and accidents. Therefore, to ensure adequate health management of the transmission system, it is necessary to investigate the friction, vibration, and dynamic properties of its contact coating surface and monitor its operating conditions

Investigating the Influence of Ball Orientation on the Foot–Ball Interaction in Rugby Union Place Kicking

Rugby Union place kicking contributes 45% of all points scored and 5.7% of matches are decided by a single kick (Quarrie and Hopkins, 2015). Biomechanical investigations of the place kick have often focused on the movements of the kicker without consideration of how the ball is orientated on the tee and whether that might interact with the kicker’s technique. Therefore, the overall aim of this thesis was to investigate how ball orientation interacts with kick technique and performance to inform the ball setup preferences of kickers. An initial study identified the ball orientation preferences of international kickers at the 2019 Rugby World Cup and assessed kick performance when kicks were categorised by ball orientation. Binomial logistic regression analysis, which also accounted for additional situational factors, revealed that kicks taken with a slanted orientation (approximately 45°) had a greater predicted kick success (90.0%) than with a forward orientation (approximately 15°; 84.4%) and a horizontal orientation (approximately 75°; 86.8%). The second study experimentally altered ball orientation to investigate the effects on kickers’ technique, impact characteristics and resulting kick performance. There were few clear effects of ball orientation on the kicking foot swing plane characteristics or the kicking leg shank and foot segment orientations at initial foot–ball impact, suggesting that each kicker maintained relatively consistent ‘end-point’ characteristics of technique. However, impact location on the ball generally varied significantly (p < 0.05) with ball orientation and when kickers struck the ball closer to the belly, impact efficiency was typically improved. This thesis provides information which could help to inform the ball orientation preferences of place kickers and coaches. There does not appear to be one ball orientation that results in the best performance for all kickers, but exploration of a ball orientation which encourages impact nearer the belly may improve impact efficiency

Application of multibody dynamics techniques to the analysis of human gait

La tesi que es presenta tracta l’estudi cinemàtic i dinàmic de la marxa humana mitjançant tècniques de dinàmica de sistemes multisòlid. Per a aquest propòsit, s’utilitzen dos models biomecànics: un model pla format per 11 segments i 14 graus de llibertat i un model tridimensional format per 18 segments i 57 graus de llibertat. La formulació dinàmica multisòlid ha estat desenvolupada en coordenades mixtes (naturals i relatives). La marxa de l’individu s’enregistra al laboratori utilitzant un sistema de captura del moviment mitjançant el qual s’obté la posició de cadascun dels 37 marcadors situats sobre el cos del subjecte. Les dades de posició es filtren utilitzant un algorisme basat en el singular spectrum analysis (SSA) i les coordenades naturals del model es calculen mitjançant relacions algebraiques entre les posicions dels marcadors. Posteriorment, un procés de consistència cinemàtica assegura les restriccions de sòlid rígid. El processament cinemàtic continua amb l’aproximació de les posicions mitjançant corbes B-spline d’on se n’obtenen, per derivació analítica, els valors de velocitat i acceleració. En una anàlisi dinàmica inversa de la marxa humana, s’acostumen a utilitzar com a dades d’entrada els paràmetres antropomètrics (geomètrics i inercials) dels segments, les dades cinemàtiques i les mesures de les plaques de força. En contraposició al que fan la majoria d’autors, en aquesta tesi, les mesures de les plaques de força no són utilitzades directament en l’anàlisi sinó que només s’usen per solucionar el problema del repartiment del torsor resultant de les forces de contacte durant la fase de doble suport. En aquesta fase, els dos peus es recolzen sobre el terra i les mesures cinemàtiques són insuficients per determinar el torsor en cada peu. El nou mètode de repartiment que es proposa (anomenat contact force plate sharing, CFP) és una de les aportacions de la tesi i destaca pel fet que permet determinar un conjunt de forces i moments dinàmicament consistents amb el model biomecànic, sense haver de modificar-ne les coordenades cinemàtiques ni afegir forces o moments residuals en algun dels segments. Encara dins l’àmbit de l’estudi dinàmic invers, s’ha analitzat la sensitivitat dels parells articulars a errors comesos en estimar els paràmetres antropomètrics, a errors que poden contenir les mesures de les plaques de força i a errors que es poden cometre en el processament cinemàtic de les mesures. L’estudi permet concloure que els resultats són molt sensibles als errors cinemàtics i a les forces mesurades per les plaques, sent els errors en els paràmetres antropomètrics menys influents. La tesi també presenta un nou model tridimensional de contacte peu-terra basat en el contacte esfera-pla i els seus paràmetres s’estimen mitjançant dos enfocaments diferents basats en tècniques d’optimització. El model s’utilitza com un mètode alternatiu per solucionar el problema del repartiment durant la fase de doble suport en dinàmica inversa, i també s’utilitza en simulacions de dinàmica directa per estimar les forces de contacte entre el model biomecànic i el seu entorn. En l’anàlisi dinàmica directa és necessària la implementació d’un controlador que està basat, en aquest cas, en el filtre de Kalman estès. Les contribucions més importants de la tesi, en el cas de l’anàlisi dinàmica inversa, es centren en el mètode CFP i en l’ús del model de contacte per solucionar el repartiment de forces de contacte en la fase de doble suport. Referent a l’anàlisi de la influència dels errors en les dades d’entrada del problema dinàmic invers, la modelització estadística dels errors conjuntament amb la pertorbació conjunta de més d’un paràmetre antropomètric a la vegada (mantenint constant l’alçada i el pes de la persona) és també una novetat. Per altra banda, el model de contacte presentat és també una contribució original. En l’estat de l’art actual no es troben models que usin dades reals capturades al laboratori i que a la vegada s’utilitzin per solucionar el problema de repartiment en el doble suport i per simular el contacte peu-terra en una anàlisi dinàmica directa. Finalment, el fet de desenvolupar un model que s’utilitzi tant per a l’anàlisi dinàmica directa com inversa és també una de les aportacions d’aquesta tesi. Tot i que les dues anàlisis, per separat, són temes de recerca comuns en l’àmbit de la Biomecànica, es troben a faltar estudis que comprovin la validesa dels resultats que se n’obtenen. En aquesta tesi, els resultats de la dinàmica inversa s’han utilitzat com a dades d’entrada de l’anàlisi dinàmica directa, el resultat de la qual (el moviment) ha pogut ser comparat amb el que s’obté de la captura del laboratori (entrada de la dinàmica inversa). D’aquesta manera, el cercle es tanca i es pot verificar la validesa tant dels models com dels resultats obtinguts.This thesis presents the kinematic and dynamic study of human motion by means of multibody system dynamics techniques. For this purpose, two biomechanical models are used: a 2D model formed by 11 segments with 14 degrees of freedom, and a 3D model that consists of 18 segments with 57 degrees of freedom. The movement of the subject is recorded in the laboratory using a motion capture system that provides the position along time of 37 markers attached on the body of the subject. Position data are filtered using an algorithm based on singular spectrum analysis (SSA) and the natural coordinates of the model are calculated using algebraic relations between the marker positions. Afterwards, a kinematic procedure ensures the kinematic consistency and the data processing continues with the approximation of the position histories using B-spline curves and obtaining, by analytical derivation, the velocity and acceleration values. This information is used as input of an inverse dynamic analysis. Differing to most published works, in this thesis the force plates measurements are not used directly as inputs of the analysis. When both feet contact the ground, kinematic measurements are insufficient to determine the individual wrench at each foot. One of the contributions of the thesis is a new strategy that is proposed to solve the this indeterminacy (called corrected force plate sharing, CFP) based on force plates data. Using this method, a set of two contact wrenches dynamically consistent with the movement are obtained with no need neither to add residual wrenches nor to modify the original motion. Also in the IDA field, the sensitivity of the joint torques to errors in the anthropometric parameters, in the force plate measurements and to errors committed during the kinematic data processing is studied. The analysis shows that the results are very sensitive to errors in force measurements and in the kinematic processing, being the errors in the body segment parameters less influential. A new 3D foot-ground contact model is presented and its parameters are estimated using optimization techniques. The model is used as an alternative method to solve the mentioned sharing problem during the double support phase and it is also used, in a forward dynamic analysis, to estimate the contact forces between the biomechanical model and its environment. The forward dynamic simulation requires the implementation of a controller that is based, in this case, on the extended Kalman filter. The most important contributions of the thesis in IDA are focused on the CFP sharing method and regarding the analysis of the influence of errors in input data on the inverse dynamics results, the statistical modelling of the uncertainties together with the perturbation of more than one parameter at same time (remaining height and weight as a constant parameters) is also new in the literature. Moreover, the presented foot-ground contact model is also original. In the current state of the art, there are no models that use real data captured in the laboratory to solve the contact wrench sharing problem during the double support phase. Furthermore, there are few studies simulating the foot-ground interaction in a forward dynamic analysis using a continuous foot-ground contact model. Finally, developing a model that is used for both forward and inverse dynamic analysis is a relevant aspect of the methodology used. Although the two approaches separately are common research topics in the field of biomechanics, a small number of studies prove the validity of the obtained results. In this thesis, the results of the inverse dynamics are used as input data for the forward dynamic analysis, and the results of the latter (the motion) have been compared with the motion capture in the laboratory (input of the inverse dynamics analysis). Thus, the circle has been closed which allows us to validate the accuracy of both the models and the obtained results

Signal processing with Fourier analysis, novel algorithms and applications

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github

Acoustic Condition Monitoring & Fault Diagnostics for Industrial Systems

Condition monitoring and fault diagnostics for industrial systems is required for cost reduction, maintenance scheduling, and reducing system failures. Catastrophic failure usually causes significant damage and may cause injury or fatality, making early and accurate fault diagnostics of paramount importance. Existing diagnostics can be improved by augmenting or replacing with acoustic measurements, which have proven advantages over more traditional vibration measurements including, earlier detection of emerging faults, increased diagnostic accuracy, remote sensors and easier setup and operation. However, industry adoption of acoustics remains in relative infancy due to vested confidence and reliance on existing measurement and, perceived difficulties with noise contamination and diagnostic accuracy. Researched acoustic monitoring examples typically employ specialist surface-mount transducers, signal amplification, and complex feature extraction and machine learning algorithms, focusing on noise rejection and fault classification. Usually, techniques are fine-tuned to maximise diagnostic performance for the given problem. The majority investigate mechanical fault modes, particularly Roller Element Bearings (REBs), owing to the mechanical impacts producing detectable acoustic waves. The first contribution of this project is a suitability study into the use of low-cost consumer-grade acoustic sensors for fault diagnostics of six different REB health conditions, comparing against vibration measurements. Experimental results demonstrate superior acoustic performance throughout but particularly at lower rotational speed and axial load. Additionally, inaccuracies caused by dynamic operational parameters (speed in this case), are minimised by novel multi-Support Vector Machine training. The project then expands on existing work to encompass diagnostics for a previously unreported electrical fault mode present on a Brush-Less Direct Current motor drive system. Commonly studied electrical faults, such as a broken rotor bar or squirrel cage, result from mechanical component damage artificially seeded and not spontaneous. Here, electrical fault modes are differentiated as faults caused by issues with the power supply, control system or software (not requiring mechanical damage or triggering intervention). An example studied here is a transient current instability, generated by non-linear interaction of the motor electrical parameters, parasitic components and digital controller realisation. Experimental trials successfully demonstrate real-time feature extraction and further validate consumer-grade sensors for industrial system diagnostics. Moreover, this marks the first known diagnosis of an electrically-seeded fault mode as defined in this work. Finally, approaching an industry-ready diagnostic system, the newly released PYNQ-Z2 Field Programmable Gate Array is used to implement the first known instance of multiple feature extraction algorithms that operate concurrently in continuous real-time. A proposed deep-learning algorithm can analyse the features to determine the optimum feature extraction combination for ongoing continuous monitoring. The proposed black-box, all-in-one solution, is capable of accurate unsupervised diagnostics on almost any application, maintaining excellent diagnostic performance. This marks a major leap forward from fine-tuned feature extraction performed offline for artificially seeded mechanical defects to multiple real-time feature extraction demonstrated on a spontaneous electrical fault mode with a versatile and adaptable system that is low-cost, readily available, with simple setup and operation. The presented concept represents an industry-ready all-in-one acoustic diagnostic solution, that is hoped to increase adoption of acoustic methods, greatly improving diagnostics and minimising catastrophic failures