Design of digital differentiators

A digital differentiator simply involves the derivation of an input signal. This work includes the presentation of first-degree and second-degree differentiators, which are designed as both infinite-impulse-response (IIR) filters and finite-impulse-response (FIR) filters. The proposed differentiators have low-pass magnitude response characteristics, thereby rejecting noise frequencies higher than the cut-off frequency. Both steady-state frequency-domain characteristics and Time-domain analyses are given for the proposed differentiators. It is shown that the proposed differentiators perform well when compared to previously proposed filters. When considering the time-domain characteristics of the differentiators, the processing of quantized signals proved especially enlightening, in terms of the filtering effects of the proposed differentiators. The coefficients of the proposed differentiators are obtained using an optimization algorithm, while the optimization objectives include magnitude and phase response. The low-pass characteristic of the proposed differentiators is achieved by minimizing the filter variance. The low-pass differentiators designed show the steep roll-off, as well as having highly accurate magnitude response in the pass-band. While having a history of over three hundred years, the design of fractional differentiator has become a ‘hot topic’ in recent decades. One challenging problem in this area is that there are many different definitions to describe the fractional model, such as the Riemann-Liouville and Caputo definitions. Through use of a feedback structure, based on the Riemann-Liouville definition. It is shown that the performance of the fractional differentiator can be improved in both the frequency-domain and time-domain. Two applications based on the proposed differentiators are described in the thesis. Specifically, the first of these involves the application of second degree differentiators in the estimation of the frequency components of a power system. The second example concerns for an image processing, edge detection application

Efficient Multiband Algorithms for Blind Source Separation

The problem of blind separation refers to recovering original signals, called source signals, from the mixed signals, called observation signals, in a reverberant environment. The mixture is a function of a sequence of original speech signals mixed in a reverberant room. The objective is to separate mixed signals to obtain the original signals without degradation and without prior information of the features of the sources. The strategy used to achieve this objective is to use multiple bands that work at a lower rate, have less computational cost and a quicker convergence than the conventional scheme. Our motivation is the competitive results of unequal-passbands scheme applications, in terms of the convergence speed. The objective of this research is to improve unequal-passbands schemes by improving the speed of convergence and reducing the computational cost. The first proposed work is a novel maximally decimated unequal-passbands scheme.This scheme uses multiple bands that make it work at a reduced sampling rate, and low computational cost. An adaptation approach is derived with an adaptation step that improved the convergence speed. The performance of the proposed scheme was measured in different ways. First, the mean square errors of various bands are measured and the results are compared to a maximally decimated equal-passbands scheme, which is currently the best performing method. The results show that the proposed scheme has a faster convergence rate than the maximally decimated equal-passbands scheme. Second, when the scheme is tested for white and coloured inputs using a low number of bands, it does not yield good results; but when the number of bands is increased, the speed of convergence is enhanced. Third, the scheme is tested for quick changes. It is shown that the performance of the proposed scheme is similar to that of the equal-passbands scheme. Fourth, the scheme is also tested in a stationary state. The experimental results confirm the theoretical work. For more challenging scenarios, an unequal-passbands scheme with over-sampled decimation is proposed; the greater number of bands, the more efficient the separation. The results are compared to the currently best performing method. Second, an experimental comparison is made between the proposed multiband scheme and the conventional scheme. The results show that the convergence speed and the signal-to-interference ratio of the proposed scheme are higher than that of the conventional scheme, and the computation cost is lower than that of the conventional scheme

The Telecommunications and Data Acquisition Report

This quarterly publication provides archival reports on developments in programs in space communications, radio navigation, radio science, and ground-based radio and radar astronomy. It reports on activities of the Deep Space Network (DSN) in planning, supporting research and technology, implementation, and operations. Also included are standardization activities at the Jet Propulsion Laboratory for space data and information systems

Seismic Correction in the Wavelet Domain

This thesis summarises novel approaches and methods in the wavelet domain employed and published in the literature by the author for the correction and processing of time-series data from recorded seismic events, obtained from strong motion accelerographs. Historically, the research developed to first de-convolve the instrument response from legacy analogue strong-motion instruments, of which there are a large number. This was to make available better estimates of the acceleration ground motion before the more problematic part of the research that of obtaining ground velocities and displacements. The characteristics of legacy analogue strongmotion instruments are unfortunately in most cases not available, making it difficult to de-couple the instrument response. Essentially this is a system identification problem presented and summarised therein with solutions that are transparent to this lack of instrument data. This was followed by the more fundamental and problematic part of the research that of recovering the velocity and displacement from the recorded data. In all cases the instruments are tri-axial, i.e. translation only. This is a limiting factor and leads to distortions manifest by dc shifts in the recorded data as a consequence of the instrument pitching, rolling and yawing during seismic events. These distortions are embedded in the translation acceleration time–series, their contributions having been recorded by the same tri-axial sensors. In the literature this is termed ‘baseline error’ and it effectively prevents meaningful integration to velocity and displacement. Sophisticated methods do exist, which recover estimates of velocity and displacement, but these require a good measure of expertise and do not recover all the possible information from the recorded data. A novel, automated wavelet transform method developed by the author and published in the earthquake engineering literature is presented. This surmounts the problem of obtaining the velocity and displacement and in addition recovers both a low-frequency pulse called the ‘fling’, the displacement ‘fling-step’ and the form of the baseline error, both inferred in the literature, but hitherto never recovered. Once the acceleration fling pulse is recovered meaningful integration becomes a reality. However, the necessity of developing novel algorithms in order to recover important information emphasises the weakness of modern digital instruments in that they are all tri- rather than sextaxial instruments