Design Of Polynomial-based Filters For Continuously Variable Sample Rate Conversion With Applications In Synthetic Instrumentati

In this work, the design and application of Polynomial-Based Filters (PBF) for continuously variable Sample Rate Conversion (SRC) is studied. The major contributions of this work are summarized as follows. First, an explicit formula for the Fourier Transform of both a symmetrical and nonsymmetrical PBF impulse response with variable basis function coefficients is derived. In the literature only one explicit formula is given, and that for a symmetrical even length filter with fixed basis function coefficients. The frequency domain optimization of PBFs via linear programming has been proposed in the literature, however, the algorithm was not detailed nor were explicit formulas derived. In this contribution, a minimax optimization procedure is derived for the frequency domain optimization of a PBF with time-domain constraints. Explicit formulas are given for direct input to a linear programming routine. Additionally, accompanying Matlab code implementing this optimization in terms of the derived formulas is given in the appendix. In the literature, it has been pointed out that the frequency response of the Continuous-Time (CT) filter decays as frequency goes to infinity. It has also been observed that when implemented in SRC, the CT filter is sampled resulting in CT frequency response aliasing. Thus, for example, the stopband sidelobes of the Discrete-Time (DT) implementation rise above the CT designed level. Building on these observations, it is shown how the rolloff rate of the frequency response of a PBF can be adjusted by adding continuous derivatives to the impulse response. This is of great advantage, especially when the PBF is used for decimation as the aliasing band attenuation can be made to increase with frequency. It is shown how this technique can be used to dramatically reduce the effect of alias build up in the passband. In addition, it is shown that as the number of continuous derivatives of the PBF increases the resulting DT implementation more closely matches the Continuous-Time (CT) design. When implemented for SRC, samples from a PBF impulse response are computed by evaluating the polynomials using a so-called fractional interval, µ. In the literature, the effect of quantizing µ on the frequency response of the PBF has been studied. Formulas have been derived to determine the number of bits required to keep frequency response distortion below prescribed bounds. Elsewhere, a formula has been given to compute the number of bits required to represent µ to obtain a given SRC accuracy for rational factor SRC. In this contribution, it is shown how these two apparently competing requirements are quite independent. In fact, it is shown that the wordlength required for SRC accuracy need only be kept in the µ generator which is a single accumulator. The output of the µ generator may then be truncated prior to polynomial evaluation. This results in significant computational savings, as polynomial evaluation can require several multiplications and additions. Under the heading of applications, a new Wideband Digital Downconverter (WDDC) for Synthetic Instruments (SI) is introduced. DDCs first tune to a signal\u27s center frequency using a numerically controlled oscillator and mixer, and then zoom-in to the bandwidth of interest using SRC. The SRC is required to produce continuously variable output sample rates from a fixed input sample rate over a large range. Current implementations accomplish this using a pre-filter, an arbitrary factor resampler, and integer decimation filters. In this contribution, the SRC of the WDDC is simplified reducing the computational requirements to a factor of three or more. In addition to this, it is shown how this system can be used to develop a novel computationally efficient FFT-based spectrum analyzer with continuously variable frequency spans. Finally, after giving the theoretical foundation, a real Field Programmable Gate Array (FPGA) implementation of a novel Arbitrary Waveform Generator (AWG) is presented. The new approach uses a fixed Digital-to-Analog Converter (DAC) sample clock in combination with an arbitrary factor interpolator. Waveforms created at any sample rate are interpolated to the fixed DAC sample rate in real-time. As a result, the additional lower performance analog hardware required in current approaches, namely, multiple reconstruction filters and/or additional sample clocks, is avoided. Measured results are given confirming the performance of the system predicted by the theoretical design and simulation

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

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

MEASUREMENT AND ANALYSIS OF SEA WAVES NEAR A REFLECTIVE STRUCTURE

Merged with duplicate record 10026.1/2047 on 06.20.2017 by CS (TIS)Methods and equipment for the measurement of ocean waves were reviewed and their suitability assessed for the aim of this project: field measurement of sea waves near a reflective coastal structure such as a breakwater. None was found to be suitable. The functional and performance objectives are set out for a new system. The evolution of the final design, based on an array of pressure sensors, is described. The whole system is intended to be deployed on the sea-bed. It is fully self contained and independent of shore based services. Located away from the surf zone it is well placed to survive storm conditions and unauthorised interference. Theoretical methods for the re-construction of surface elevation records from measured sub-surface pressures, and the experimental findings of other workers, are presented. Available methods of estimating the wave directional spectrum from a spatial array of surface elevation records are reviewed, and the most appropriate one implemented. The system has given extensive service at a number of coastal defence sites. The results of subsequent analysis of selected data sets are presented in detail. They show the pronounced nodal structure in amplitude expected in the presence of wave reflection, clearly demonstrating that a single point measurement is likely to give misleading estimates of incident wave height. For near-calm to moderate, shore-normal incident wave conditions the results were found to agree with theoretical predictions both of wave height as a function of distance offshore, and of the structure's frequency-dependent reflection coefficient. For rougher conditions, in which both theoretical and physical models are less applicable, the results agreed with visual observations

Multidimensional Wavelets and Computer Vision

This report deals with the construction and the mathematical analysis of multidimensional nonseparable wavelets and their efficient application in computer vision. In the first part, the fundamental principles and ideas of multidimensional wavelet filter design such as the question for the existence of good scaling matrices and sensible design criteria are presented and extended in various directions. Afterwards, the analytical properties of these wavelets are investigated in some detail. It will turn out that they are especially well-suited to represent (discretized) data as well as large classes of operators in a sparse form - a property that directly yields efficient numerical algorithms. The final part of this work is dedicated to the application of the developed methods to the typical computer vision problems of nonlinear image regularization and the computation of optical flow in image sequences. It is demonstrated how the wavelet framework leads to stable and reliable results for these problems of generally ill-posed nature. Furthermore, all the algorithms are of order O(n) leading to fast processing

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

SYNTHESIS AND CHARACTERIZATION OF ENERGETIC NANOMATERIALS WITH TUNABLE REACTIVITY FOR PROPULSION APPLICATIONS

Combustion is the world’s leading energy conversion method in which a fuel and oxidizer react and release energy, typically in the form of heat. Energetic materials (propellants, pyrotechnics, and explosives) have combustion reactions that are so fast that they are generally limited by how quickly the fuel and oxidizer can reach each other. Recent research has employed nanomaterials to reduce the distance between reactants to increase energy release rates. This dissertation attempts to uncover and quantify structure-function relationships in energetic nanomaterials by modifying chemical and physical properties of the materials and characterizing the observed changes using new diagnostic tools. This dissertation begins with the development of diagnostic tools that can capture the dynamics of energetic material combustion using a high-speed color camera to measure temperature. This tool has also been modified into a high-speed microscope that allows for spatial and temperature measurements at microscale length (µm) and time (µs) scales. Changes to chemical formula have been explored for energetic nanomaterial systems, though visualization of the reaction dynamics limited detailed results on reaction mechanisms. The first study performed here probed the role of gas generation vs. thermal effects in energy release rate where it was found that combustion inefficiencies from reactive sintering could be mitigated by introducing a gas-generating oxidizer. To explore combustion improvements in the fuel, a metal fuel nanoparticle manufacturing method was explored, though the combustion performance was again limited by reactive sintering. Another effort to reduce reactive sintering with a gas generator proved successful, but also unveiled the importance of different heat transfer mechanisms for propagation. The role of physical architecture on propellant combustion was also investigated to improve efficiency and versatility in solid propellants. It was found that addition of a poor thermal conductor to a propellant mixture increased the propagation rate of the material and this was attributed to the result increase in burning surface area resulting from inhomogeneous heat transfer. Lastly, this dissertation explores a method to remotely ignite materials using microwaves and titanium nanoparticles. This work sets the stage for a remotely staged solid propellant architecture that would provide control over solid propellant combustion in-operando