Several new algorithms are presented for the optimal approximation and design of various classes of digital filters. An iterative algorithm is developed for the efficient design of unconstrained and constrained infinite impulse response (IIR) digital filters. Both in the unconstrained and constrained cases, the numerator and denominator of the filter transfer function are designed iteratively by recourse to the Remez algorithm and to appropriate design parameters and criteria, at each iteration. This makes it possible for the algorithm to be implemented by means of a short main program which uses (at each iteration) the linear phase FIR filter design algorithm of McClellan et al. as a subroutine. The approach taken also permits the filter to be designed with a desired ripple ratio. Also, the algorithm determines automatically the minimum passband ripple corresponding to the prescribed orders and band edges of the filter. The filter is designed directly without guessing the passband ripple or stopband ripple. Another algorithm, based on similar principles, is developed for the design of a nonlinear phase finite impulse response (FIR) filter, whose transfer function optimally approximates a desired magnitude response, there being no constraints imposed on the phase response. A similar algorithm is presented for the design of two new classes of FIR digital filters, one linear phase and the other nonlinear phase. A filter of either class has significantly reduced number of multiplications compared to the one obtained by its conventional counterpart, with respect to a given frequency response. In the case of linear phase, by introducing the new class of digital filters into the design of multistage decimators and interpolators for narrow-band filter implementation, it is found that an efficient narrow-band filter requiring considerably lower multiplication rate than the conventional linear phase FIR design can be obtained. The amount of data storage required by the new class of nonlinear phase FIR filters is significantly less than its linear phase counterpart. Finally, the design of a (finite-impulse-response) FIR digital filter with some of the coefficients constrained to zero is formulated as a linear programming (LP) problem and the LP technique is then used to design this class of constrained FIR digital filters. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI

Polysilicon is believed to be a key element for continued evolution of silicon integrated circuits. Recent advances in radiation processing and passivation techniques have enhanced the possibility of realizing acceptable active devices in polysilicon thin films. Of late, MOS devices fabricated in polysilicon do hold up a distinct possibility of achieving 3-D integration for higher packing density. P-n junction diode constitutes an essential element of any device. It is therefore imperative to have a quantitative model of p-n junction diodes in polysilicon. In this thesis, a model for the polysilicon p-n junction diodes is developed. The present model is based on incorporating the effective minority carrier lifetime operative in crystalline grain and amorphous conducting boundary. The bulk resistance effect especially at lower doping levels is accounted for. In addition, in the present model, the grain boundaries parallel to the current flow in the junction depletion depth are shown to serve as ohmic conduction channels. This additional amorphous channel can account for the unusually high current level observed at small applied voltages. The role of grain boundary in affecting minority carrier diffusion processes is illustrated by considering the presence of one grain boundary in the analysis of continuity equation operative in minority carrier diffusion region.

Four methods for designing digital filters optimal in the Chebyshev sense are developed. The properties of these filters are investigated and compared. An analytic method for designing narrow-band FIR filters using Zolotarev polynomials, which are extensions of Chebyshev polynomials, is proposed. Bandpass and bandstop narrow-band filters as well as lowpass and highpass filters can be designed by this method. The design procedure, related formulae and examples are presented. An improved method of designing optimal minimum phase FIR filters by directly finding zeros is proposed. The zeros off the unit circle are found by an efficient special purpose root-finding algorithm without deflation. The proposed algorithm utilizes the passband minimum ripple frequencies to establish the initial points, and employs a modified Newton's iteration to find the accurate initial points for a standard Newton's iteration. The proposed algorithm can be used to design very long filters (L = 325) with very high stopband attenuations. The design of FIR digital filters in the complex domain is investigated. The complex approximation problem is converted into a near equivalent real approximation problem. A standard linear programming algorithm is used to solve the real approximation problem. Additional constraints are introduced which allow weighting of the phase and/or group delay of the approximation. Digital filters are designed which have nearly constant group delay in the passbands. The desired constant group delay which gives the minimum Chebyshev error is found to be smaller than that of a linear phase filter of the same length. These filters, in addition to having a smaller, approximately constant group delay, have better magnitude characteristics than exactly linear phase filters with the same length. The filters have nearly equiripple magnitude and group delay. The problem of IIR digital filter design in the complex domain is formulated such that the existence of best approximation is guaranteed. An efficient and numerically stable algorithm for the design is proposed. The methods to establish a good initial point are investigated. Digital filters are designed which have nearly constant group delay in the passbands. The magnitudes of the filter poles near the passband edge are larger than of those far from the passband edge. A delay overshooting may occur in the transition band (don't care region), and it can be reduced by decreasing the maximum allowed pole magnitude of the design problem at the expense of increasing the approximation error.

Indium Phosphide epitactic layers grown by MOCVD and lightly doped with Zn and Mg (p-type) have been studied by Hall effect measurements and secondary ion mass spectroscopy (SIMS). The Zn-doped samples showed a uniform distribution of the acceptor concentration as a function of depth. Mg doped samples showed strong Mg concentration gradients, with substantial diffusion into the substrate. An electrical transport model has been developed for each of the previous cases. These models provided excellent agreement with experiment. The uniformly Zn-doped samples have been used for a detailed study of hopping conduction. Excellent quantitative agreement can be reached between theory and experiment both in the variable range hopping regime and in the nearest neighbor hopping regime. The saturation of the latter regime has been observed, and a model has been found in qualitative agreement with it. An interpretation of the low temperature data on the basis of the presence of a Coulomb gap in the impurity band density of states is not appropriate.

A gas-solid reaction analyzer was built in order to study the kinetics of various interesting gas-solid reactions, including the interstitial modification kinetics of carbonitride magnets. The system performs an analysis of the pressure and temperature of the carbonitride during the interstitial modification, as well as performing atomic mass analysis of the gases present throughout the gas-solid reaction. / All the hardware, software, and electronics that make up the system were constructed as part of the requirements for the M.Sc. thesis, with the exception of the Quadrupole Mass Spectrometer (QMS) and the Transpector electronics unit which shipped with the mass spectrometer.

The design and construction of a capacitor-discharge pulsed magnet is described. The magnet is capable of generating peak fields up to 22 T in a multi-turn solenoid coil with a 3/4" (19 mm) bore. The coil design, calculation of peak field, and an analysis of the eddy currents in the metal surrounding the coil are discussed in detail. The pulsed magnet includes a magnetometer and a data acquisition system which measure the coil field and sample magnetization. A series of magnetization curves have been obtained for a sample of Nd$ rm{ sb2 Fe sb{14} B}$.

In this thesis, we develop a first principle technique to study linear AC and the nonlinear DC quantum transport in diffusive conductors. Starting from Buttiker's theory for AC and DC transport, the emittance and nonlinear DC conductance are found in terms of the scattering matrix and it's functional derivative. New theoretical tools are developed to compute the functional derivative of the scattering matrix, which would otherwise be unaccessible. These results allows us to compute the linear AC and the nonlinear DC conductance for a diffusive conductor from first principles, for the first time in literature. The sample-to-sample AC conductance fluctuations are computed for a diffusive conductor. In this regime the dynamic response of the conductor can either be capacitive or inductive, depending on impurity configuration. Our results also suggest a crossover for the AC conductance distribution, from a symmetric to a non symmetric distribution function as the number of impurities increases. A degree of generic behavior is discovered, in that the AC fluctuation amplitudes become independent of the strength of the impurities, although it depends on the impurity density. A sample-to-sample analysis of the nonlinear conductance fluctuations, in the diffusive regime, is also reported. In this situation the distribution function is found to be a symmetric Gaussian like function for small disorder and a symmetric exponentially decaying function for large disorder. An interesting result is that the conductance fluctuations increase in an exponential fashion with N, the number of impurities. / We also considered in this thesis the magneto-conductance fluctuations of a quasi-1D quantum wire with artificial impurities (antidots). This problem can only be solved numerically because of the finite size of the artificial impurities. We develop a novel transfer matrix technique to solve the quantum scattering problem by computing the scattering wave function, as a function of the external magnetic field. The Landauer-Buttiker equation is used to compute the magneto-conductance. This work is motivated by the experimental study [1], where several conductance fluctuations anomalies were reported. Our numerical results give good quantitative agreement with the experimental data and confirms the physical picture obtained from the experiment.

Measurements of the spin-lattice relaxation time, T1, and spin-spin relaxation time, T2, of potassium ferricyanide diluted by potassium coba1ticyanide were made by the CW saturation method. Crystals of two concentrations of Fe3+ in K3Co(CN)6 were investigated: 0.5% and 1.0%. The results are the same for both concentrations to within the probable error. The mean relaxation times for the two concentrations are quoted to one significant figure, together with the probable errors: T1 =(1 +- 0.15) x 10-4 sec and T2 = (9 +- 0.4) x 10-9 sec. Calculations have been made to determine the angular dependence of the paramagnetic resonance spectra of potassium ferricyanide. Three graphs have been plotted which may be useful for comparison with future measurements.

A current-switched superconducting field-cycling NMR spectrometer has been designed and built for studying the role of quantum tunnelling in molecular dynamics. The instrument is designed for work in the solid state with sample temperatures extending from 4K up to 300K. The maximum field-switching rate is 10Ts-1. Among the samples studied in this thesis is the nuclear spin-relaxation and proton tunnelling. Concerted double proton transfer in the hydrogen bonds of carboxylic acid dimers is well established as the model system for translational quantum tunnelling. The model system has been chosen to illustrate the smooth quantum-to-classical transition and at all temperatures the proton transfer is characterised by a single correlation time. Quadrupolar interactions introduce an additional relaxation to the proton spin polarisation. The enhanced relaxation of the proton spin appears as a dip in the proton magnetisation curve. This technique is employed to measure the quadrupolar transition frequency of 14N and 35Cl and determine the structure of heroin hydrochloride. The introduction of a second spin species has a significant effect on the spin-lattice relaxation. Compared with homonuclear systems, the spectral density acquires additional components characterised by the sum and difference Larmor frequencies of the two nuclei. Further, instead of a single relaxation time, there are four elements of a relaxation matrix. Therefore, the magnetisation recovery becomes bi-exponential and the initial polarisation state of the second nucleus strongly affects the magnetisation recovery of the nucleus which is being observed. We shall report on the results of spin-lattice relaxation investigations on 1H-13C, 1H-19F systems. The role of heteronuclear interactions in spin-lattice relaxation and the newly developed methodology of field-cycling relaxometry will be discussed. This represents the first 13C field-cycling NMR experiment and the first to measure the field dependence of the off-diagonal element of the relaxation matrix.

The technique of functional magnetic resonance imaging is rapidly moving from one of technical interest to wide clinical application. However, there are a number of questions regarding the method that need resolution. Some of these are investigated in this thesis. High resolutionf MRI is demonstrated at 3.0 T, using an interleaved echo planar imaging technique to keep image distortion low. The optimum echo time to use in fMRI experiments is investigated using a multiple gradient echo sequence to obtain six images, each with a different echo time, from a single free induction decay. The same data are used to construct T2* maps during functional stimulation. Various techniques for correcting the N/2 ghost are tested for use in fMRI experiments, and a method for removing the image artefact caused by external r. f. interference in a non-linearly sampled matrix is presented. The steps in the analysis of fMRI data are detailed, and two new non-directed analysis techniques, particularly for data from single events, as opposed to epoch based paradigms, are proposed. The theory behind software that has been written for fMRI data analysis is also given. Finally, some of the results from an fMRI study into the initiation of movement are presented, illustrating the power of single event experiments in the separation of cognitive processes.