The investigation into three types of dielectric resonators for use in base-station filtering applications is presented. The triple-mode cubic TE016 resonator is shown to have good performance for high Q applications. Its suitability for realising conventional narrowband selective bandpass filter responses is proved. The effect on the response of spurious intercavity couplings through irises is studied. The triple-mode cubic TE016 resonator is also used for the realisation of a novel type of filter, the even-odd hybrid mode reflection filter, which eliminates the need for cross-couplings for any symmetrical frequency response. The insensitivity of the new type of filter to most spurious couplings is shown in the case of a sixth degree elliptic filter. The drawbacks of this type of filter are also described. The new dual-mode conductor-loaded dielectric resonator is presented. An exact model of the resonator is necessary for an accurate study of this resonator. The axial mode-matching technique is used. The relative numbers of modes to use in each section of the model for optimum convergence primarily depend on the mode type and the relative diameters of the dielectric cylinder and the metal disc. The convergence of the resonant frequencies is good. That of the quality factors is slower but still provide useful approximate results. These convergences are affected respectively by large electric and magnetic field amplitudes in singularity regions. The resonant frequency and Q. of the fundamental mode are primarily dependent on the diameter and height of the dielectric cylinder respectively. The resonator geometry is optimised for Qu and spurious separation at 900 MHz and trade-offs between the two criteria are quantified. The resonator is found to be particularly suited for medium Q applications, i. e. between 4000 and 7000. The third resonator, the dielectric-loaded TEO,, resonator, is shown to be well suited for applications around 2 GHz and requiring Qu's of a few thousands. Theoptimum cavity cross-section dimensions for maximum Qu volume are almost constant over a wide range of cavity diameters. The trade-off between Qu and spurious separation is explained. Coupling bandwidth limitations in the case of off-line cavities are found to be solvable by using off-centred resonators. 80 MHz wide filters, optimised for ease of manufacturing, are built.

This thesis develops a new theory of tuning filters based on the time-domain response of the filter. These methods are shown to work very well for all-pole coupledresonator filters in particular, and may be applied to automated tuning of filters. Numerous filter-tuning methods are reviewed, and the attributes and limitations of each are discussed. Key results about transfer functions, filter theory and Laplace transform theory are reviewed as applied to all-pole filters. The Fourier Transform theory is reviewed and a new, detailed analysis of the Vector Network Analyzer (VNA) time-domain transform, including gating and windowing is presented, including new work in area of the compensation for the masking effects of time-domain gating. A complete description of the time-domain tuning method is presented, which includes experimental and empirical results from simulations and measurements on filters. The theoretical underpinning supporting the novel method of time-domain tuning is developed, along with a rigorous mathematical relationship between VNA timedomain response of a simple filter, and the analytic impulse response. The timedomain results observed in experiments are shown to be directly correlated to the filter transfer functions and the specific effects that differentiate the VNA time-domain transform from the analytically derived impulse response. This thesis includes previously unpublished work that is the basis for two U.S. patents, as well as the development of a commercial filter tuning software program. An improved method for filter tuning, which uses time-domain gating on the S 11 response of the filter is introduced, and shown to be a key improvement for developing automated tuning techniques. The details of a software application for filter tuning are presented, along with methods for determining and compensating the interactions from other resonators. A case study of applying the FTS method to a complex duplex filter is described. Areas for extension into other filter types are discussed. General guidelines for the successful application of the new tuning method to various filter types are presented, along with other conclusions of this thesis.

One-dimensional (I-D) and two-dimensional (2-D) frequency-space seismic migration FIR digital filter coefficients are of complex values when such filters require special space domain as well as wavenumber domain characteristics. In this thesis, such FIR digital filters are designed using Vector Space Projection Methods (VSPMs), which can satisfy the desired predefined filters' properties, for 2-D and three-dimensional (3-D) seismic data sets, respectively. More precisely, the pure and the relaxed projection algorithms, which are part of the VSPM theory, are derived. Simulation results show that the relaxed version of the pure algorithm can introduce significant savings in terms of the number of iterations required. Also, due to some undesirable background artifacts on migrated sections, a modified version of the pure algorithm was used to eliminate such effects. This modification has also led to a significant reduction in the number of computations when compared to both the pure and relaxed algorithms. We further propose a generalization of the l-D (real/complex-valued) pure algorithm to multi-dimensional (m-D) complex-valued FIR digital filters, where the resulting frequency responses possess an approximate equiripple nature. Superior designs are obtained when compared with other previously reported methods. In addition, we also propose a new scheme for implementing the predesigned 2-D migration FIR filters. This realization is based on Singular Value Decomposition (SVD). Unlike the existing realization methods which are used for this geophysical application, this cheap realization via SVD, compared with the true 2-D convolution, results in satisfactory wavenumber responses. Finally, an application to seismic migration of 2-D and 3-D synthetic sections is shown to confirm our theoretical conclusions. The proposed resulting migration FIR filters are applied also to the challenging SEGIEAGE Salt model data. The migrated section (image) outperformed images obtained using other FIR filters and with other standard migration techniques where difficult structures contained in such a challenging model are imaged clearly.

Advances in vector sensor technology have created a need for adaptive nonlinear signal processing in the quaternion domain. The main concern of this thesis lies in the issue of analyticity of quaternion-valued nonlinear functions. The Cauchy-Riemann-Fueter (CRF) conditions determine the analyticity in the quaternion domain which proved too strict to be of any practical use. In order to circumvent this problem, split-quaternion nonlinear functions which are analytic componentwise are commonly employed. However, these functions do not fully capture the correlations between dimensions and are not suitable for real-world applications. To address this, the use of fully quaternion nonlinear functions in the derivation of a completely new class of algorithms which takes into consideration the non-commutative aspect of quaternion product is proposed. These fully quaternion functions satisfy the local analyticity condition (LAC) that guarantees the first-order differentiability of the function. This provides a unifying framework for the derivation of gradient based learning algorithms in the quaternion domain which are shown to have the same generic form as their real- and complex-valued counterparts. Unlike existing approaches, this new class of algorithms derived is suitable for the processing of signals with strong component correlations and is further extended to the recurrent neural network (RNN) architecture. Novel algorithms are also derived to improve the computational complexity of quaternion-valued adaptive filters which could be easily extended to incorporate nonlinear functions. A rigorous mathematical analysis provides a basis for the understanding of the convergence and steady-state performance of the proposed algorithms. Simulations over a range of synthetic and real-world signals support the approach taken in the thesis.

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