Hardward and algorithm architectures for real-time additive synthesis

Additive synthesis is a fundamental computer music synthesis paradigm tracing its origins to the work of Fourier and Helmholtz. Rudimentary implementation linearly combines harmonic sinusoids (or partials) to generate tones whose perceived timbral characteristics are a strong function of the partial amplitude spectrum. Having evolved over time, additive synthesis describes a collection of algorithms each characterised by the time-varying linear combination of basis components to generate temporal evolution of timbre. Basis components include exactly harmonic partials, inharmonic partials with time-varying frequency or non-sinusoidal waveforms each with distinct spectral characteristics. Additive synthesis of polyphonic musical instrument tones requires a large number of independently controlled partials incurring a large computational overhead whose investigation and reduction is a key motivator for this work. The thesis begins with a review of prevalent synthesis techniques setting additive synthesis in context and introducing the spectrum modelling paradigm which provides baseline spectral data to the additive synthesis process obtained from the analysis of natural sounds. We proceed to investigate recursive and phase accumulating digital sinusoidal oscillator algorithms, defining specific metrics to quantify relative performance. The concepts of phase accumulation, table lookup phase-amplitude mapping and interpolated fractional addressing are introduced and developed and shown to underpin an additive synthesis subclass - wavetable lookup synthesis (WLS). WLS performance is simulated against specific metrics and parameter conditions peculiar to computer music requirements. We conclude by presenting processing architectures which accelerate computational throughput of specific WLS operations and the sinusoidal additive synthesis model. In particular, we introduce and investigate the concept of phase domain processing and present several “pipeline friendly” arithmetic architectures using this technique which implement the additive synthesis of sinusoidal partials

Analog Implementation of Fractional-Order Elements and Their Applications

With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received considerable attention. This is due to the fact that this powerful mathematical tool allows us to describe and model a real-world phenomenon more accurately than via classical “integer” methods. Moreover, their additional degree of freedom allows researchers to design accurate and more robust systems that would be impractical or impossible to implement with conventional capacitors. Throughout this thesis, a wide range of problems associated with analog circuit design of fractional-order systems are covered: passive component optimization of resistive-capacitive and resistive-inductive type fractional-order elements, realization of active fractional-order capacitors (FOCs), analog implementation of fractional-order integrators, robust fractional-order proportional-integral control design, investigation of different materials for FOC fabrication having ultra-wide frequency band, low phase error, possible low- and high-frequency realization of fractional-order oscillators in analog domain, mathematical and experimental study of solid-state FOCs in series-, parallel- and interconnected circuit networks. Consequently, the proposed approaches in this thesis are important considerations in beyond the future studies of fractional dynamic systems

Denoising and enhancement of digital images : variational methods, integrodifferential equations, and wavelets

The topics of this thesis are methods for denoising, enhancement, and simplification of digital image data. Special emphasis lies on the relations and structural similarities between several classes of methods which are motivated from different contexts. In particular, one can distinguish the methods treated in this thesis in three classes: For variational approaches and partial differential equations, the notion of the derivative is the tool of choice to model regularity of the data and the desired result. A general framework for such approaches is proposed that involve all partial derivatives of a prescribed order and experimentally are capable of leading to piecewise polynomial approximations of the given data. The second class of methods uses wavelets to represent the data which makes it possible to understand the filtering as very simple pointwise application of a nonlinear function. To view these wavelets as derivatives of smoothing kernels is the basis for relating these methods to integrodifferential equations which are investigated here. In the third case, values of the image in a neighbourhood are averaged where the weights of this averaging can be adapted respecting different criteria. By refinement of the pixel grid and transfer to scaling limits, connections to partial differential equations become visible here, too. They are described in the framework explained before. Numerical aspects of the simplification of images are presented with respect to the NDS energy function, a unifying approach that allows to model many of the aforementioned methods. The behaviour of the filtering methods is documented with numerical examples.Gegenstand der vorliegenden Arbeit sind Verfahren zum Entrauschen, qualitativen Verbessern und Vereinfachen digitaler Bilddaten. Besonderes Augenmerk liegt dabei auf den Beziehungen und der strukturellen Ähnlichkeit zwischen unterschiedlich motivierten Verfahrensklassen. Insbesondere lassen sich die hier behandelten Methoden in drei Klassen einordnen: Bei den Variationsansätzen und partiellen Differentialgleichungen steht der Begriff der Ableitung im Mittelpunkt, um Regularität der Daten und des gewünschten Resultats zu modellieren. Hier wird ein einheitlicher Rahmen für solche Ansätze angegeben, die alle partiellen Ableitungen einer vorgegebenen Ordnung involvieren und experimentell auf stückweise polynomielle Approximationen der gegebenen Daten führen können. Die zweite Klasse von Methoden nutzt Wavelets zur Repräsentation von Daten, mit deren Hilfe sich Filterung als sehr einfache punktweise Anwendung einer nichtlinearen Funktion verstehen lässt. Diese Wavelets als Ableitungen von Glättungskernen aufzufassen bildet die Grundlage für die hier untersuchte Verbindung dieser Verfahren zu Integrodifferentialgleichungen. Im dritten Fall werden Werte des Bildes in einer Nachbarschaft gemittelt, wobei die Gewichtung bei dieser Mittelung adaptiv nach verschiedenen Kriterien angepasst werden kann. Durch Verfeinern des Pixelgitters und Übergang zu Skalierungslimites werden auch hier Verbindungen zu partiellen Differentialgleichungen sichtbar, die in den vorher dargestellten Rahmen eingeordnet werden. Numerische Aspekte beim Vereinfachen von Bildern werden anhand der NDS-Energiefunktion dargestellt, eines einheitlichen Ansatzes, mit dessen Hilfe sich viele der vorgenannten Methoden realisieren lassen. Das Verhalten der einzelnen Filtermethoden wird dabei jeweils durch numerische Beispiele dokumentiert

Engineering Education and Research Using MATLAB

MATLAB is a software package used primarily in the field of engineering for signal processing, numerical data analysis, modeling, programming, simulation, and computer graphic visualization. In the last few years, it has become widely accepted as an efficient tool, and, therefore, its use has significantly increased in scientific communities and academic institutions. This book consists of 20 chapters presenting research works using MATLAB tools. Chapters include techniques for programming and developing Graphical User Interfaces (GUIs), dynamic systems, electric machines, signal and image processing, power electronics, mixed signal circuits, genetic programming, digital watermarking, control systems, time-series regression modeling, and artificial neural networks

A geometric and physical study of Riemann's non-diferentiable function.

167 p.Riemann's non-differentiable function is a classic example of a continuous but almost nowheredifferentiable function, whose analytic regularity has been widely studied since it was proposedin the second half of the 19th century. But recently, strong evidence has been found that one ofits generalisation to the complex plane can be regarded as the trajectory of a particle in thecontext of the evolution of vortex filaments. It can, thus, be given a physical and geometricinterpretation, and many questions arise in these settings accordingly.It is the purpose of this dissertation to describe, study and prove geometrically and physicallymotivated properties of Riemann's non-differentiable function. In this direction, a geometricanalysis of concepts such as the Hausdorff dimension, geometric differentiability and tangentswill be carried out, and the relationship with physical phenomena such as the Talbot effect,turbulence, intermittency and multifractality will be explained

A geometric and physical study of Riemann's non-differentiable function

Riemann's non-differentiable function is a classic example of a continuous but almost nowhere differentiable function, whose analytic regularity has been widely studied since it was proposed in the second half of the 19th century. But recently, strong evidence has been found that one of its generalisation to the complex plane can be regarded as the trajectory of a particle in the context of the evolution of vortex filaments. It can, thus, be given a physical and geometric interpretation, and many questions arise in these settings accordingly. It is the purpose of this dissertation to describe, study and prove geometrically and physically motivated properties of Riemann's non-differentiable function. In this direction, a geometric analysis of concepts such as the Hausdorff dimension, geometric differentiability and tangents will be carried out, and the relationship with physical phenomena such as the Talbot effect, turbulence, intermittency and multifractality will be explained.Ministerio de Educación, Cultura y Deporte - FPU15/0307

Channelization for Multi-Standard Software-Defined Radio Base Stations

As the number of radio standards increase and spectrum resources come under more pressure, it becomes ever less efficient to reserve bands of spectrum for exclusive use by a single radio standard. Therefore, this work focuses on channelization structures compatible with spectrum sharing among multiple wireless standards and dynamic spectrum allocation in particular. A channelizer extracts independent communication channels from a wideband signal, and is one of the most computationally expensive components in a communications receiver. This work specifically focuses on non-uniform channelizers suitable for multi-standard Software-Defined Radio (SDR) base stations in general and public mobile radio base stations in particular. A comprehensive evaluation of non-uniform channelizers (existing and developed during the course of this work) shows that parallel and recombined variants of the Generalised Discrete Fourier Transform Modulated Filter Bank (GDFT-FB) represent the best trade-off between computational load and flexibility for dynamic spectrum allocation. Nevertheless, for base station applications (with many channels) very high filter orders may be required, making the channelizers difficult to physically implement. To mitigate this problem, multi-stage filtering techniques are applied to the GDFT-FB. It is shown that these multi-stage designs can significantly reduce the filter orders and number of operations required by the GDFT-FB. An alternative approach, applying frequency response masking techniques to the GDFT-FB prototype filter design, leads to even bigger reductions in the number of coefficients, but computational load is only reduced for oversampled configurations and then not as much as for the multi-stage designs. Both techniques render the implementation of GDFT-FB based non-uniform channelizers more practical. Finally, channelization solutions for some real-world spectrum sharing use cases are developed before some final physical implementation issues are considered

Analysis and Design of Low-Cost Waveguide Filters for Wireless Communications

The area of research of this thesis is built around advanced waveguide filter structures. Waveguide filters and the waveguide technology in general are renowned for high power capacity, low losses and excellent electromagnetic shielding. Waveguide filters are important components in fixed wireless communications as well as in satellite and radar systems. Furthermore, their advantages and utilization become even greater with increase in frequency, which is a trend in modern communication systems because upper frequency bands offer larger channel capacities. However, waveguide filters are relatively bulky and expensive. To comply with more and more demanding miniaturization and cost-cutting requirements, compactness and economical design represent some of the main contemporary focuses of interest. Approaches that are used to achieve this include use of planar inserts to build waveguide discontinuities, additive manufacturing and substrate integration. At the same time, waveguide filters still need to satisfy opposed stringent requirements like small insertion loss, high selectivity and multiband operation. Another difficulty that metal waveguide components face is integration with other circuitry, especially important when solid-state active devices are included. Thus, improvements of interconnections between waveguide and other transmission interfaces are addressed too. The thesis elaborates the following aspects of work: Further analysis and improved explanations regarding advanced waveguide filters with E-plane inserts developed by the Wireless Communications Research Group, using both cross coupled resonators and extracted pole sections (Experiments with higher filter orders, use of tuning screws, degrees of freedom in design, etc. Thorough performance comparison with competing filter technologies) - Proposing novel E-plane filter sections with I-shaped insets - Extension of the E-plane filtering structures with metal fins to new compact dual band filters with high frequency selectivity and miniaturized diplexers. - Introduction of easy-to-build waveguide filters with polymer insert frames and high-performance low-profile cavity filters, taking advantage of enhanced fabrication capabilities when using additive manufacturing - Developing new substrate integrated filters, as well as circuits used to transfer signals between different interfaces Namely, these are substrate integrated waveguide to metal waveguide planar transitions that do not require any modifications of the metal waveguides. Such novel transitions have been designed both for single and orthogonal signal polarizations