Mathematics Commons^™

Representations, Approximations, And Algorithms For Mathematical Speech Processing, Laura R. Suzuki

Theses and Dissertations

Representing speech signals such that specific characteristics of speech are included is essential in many Air Force and DoD signal processing applications. A mathematical construct called a frame is presented which captures the important time-varying characteristic of speech. Roughly speaking, frames generalize the idea of an orthogonal basis in a Hilbert space, Specific spaces applicable to speech are L₂(R) and the Hardy spaces H_p(D) for p> 1 where D is the unit disk in the complex plane. Results are given for representations in the Hardy spaces involving Carleson's inequalities (and its extensions), …

A Non-Homogeneous, Spatio-Temporal, Wavelet Multiresolution Analysis And Its Application To The Analysis Of Motion, Thomas J. Burns

Theses and Dissertations

This research presents a multiresolution wavelet analysis tool for analyzing motion in time sequential imagery. A theoretical framework is developed for constructing an L2R wavelet multiresolution analysis from three non-identical spatial and temporal L2R wavelet multiresolution analyses. This framework provides the flexibility to tailor the spatio-temporal frequency characteristics of the three dimensional wavelet filter to match the frequency behavior of the analyzed signal. An unconventional, discrete multiresolution wavelet decomposition algorithm is developed which yields a rich set of independent spatio-temporally oriented frequency channels for analyzing, the size and speed characteristics of moving objects. Unlike conventional wavelet decomposition methods, this algorithm …

Frequency Domain Speech Compression Using The Karhunen-Loeve Transform, Donald W. Dryley

Theses and Dissertations

The purpose of this study was test the influence of phase on the quality of speech reproduced by a speaker dependent compression system. The tests consisted of compressing frequency domain speech vectors using the Karhunen-Loeve Transform, with and without phase, then making subjective judgements as to the reproduced quality. Error Metrics were then tested for their suitability as predictors of reproduced quality. The compression software transformed each speech vector into a vector of complex Fourier coefficients (only half of the coefficients are needed as transform is hermitian). Phase was preserved by using the real frequency components to form one vector …

Discrete Simulation Of Fractional Order Systems, Jeffrey A. Blank

Theses and Dissertations

Fractional calculus has been shown useful for describing many real world systems, and studies are currently underway to generalize control theory to incorporate fractional states. This investigation derives a method for simulating the time response of fractional order systems using a recursive difference equation. The technique used effectively approximates a simple fractional order integrator as a summation of integer order terms. The discrete transfer function is also derived and the frequency response of the discrete algorithm is compared to the exact continuous case. Using 20 or more retained past values in the difference equation, the discrete half-order integrator demonstrates a …

The Design And Implementation Of A Tutorial Program To Perform Symbolic Mathematics, Richard Derek Otieno

Theses and Dissertations

The purpose of this thesis is to design and implement a program that could be used for a drill in symbolic mathematics. The scope of the program with respect to the range of problems that it solves is limited to selected types from elementary algebra, trigonometry, differential calculus, and integral calculus. The program is designed, not only to give solutions (answers), but also to provide several of the intermediate steps leading to the final result.

FORMAC73 and PL/1 are used to implement the program. FORMAC73 is a system and a language for manipulating mathematical expressions, symbolically. The facilities of PL/1 …

A Comparison Of Processor Technologies, Eddie R. Wachter

Theses and Dissertations

The purpose of this paper is to present a discussion of the technology implementation and design of four very high performance mainframe computer systems. The systems evaluated are:

Amdahl 580 Series

CDC 170 Series 800

IBM 308x Series

Univac 1100/90 Series

Included in this evaluation is a survey of the technology used, its characteristics, packaging and performance. Each system component is evaluated on the basis of design philosophy, technology, and the total system design with regards to reliability, availability, and performance.

A Modified Crank-Nicolson Method, Ernest David Jordan Jr.

Theses and Dissertations

In order to obtain a numerical solution to the heat equation using finite differences, either implicit or explicit equations are used to formulate a solution. The advantage in an explicit formulation is its simplicity and minimal computer storage requirements while its disadvantage is its instability. The opposite is true for an implicit formulation such as the Crank-Nicolson method; although it is stable it is more difficult to implement and requires a much larger memory capacity. In this paper we examine the accuracy and stability of a hybrid approach, a modified Crank-Nicolson formulation, that combines the advantageous features of both the …

Calculation Of Galois Groups, Daniel Schnackenberg

Theses and Dissertations

In the 19th Century Galois developed a method for determining whether an equation is solvable. It relied on the close relationship between fields and their automorphism group. This paper is a survey of the techniques of Galois theory. After presenting the main results of elementary Galois theory and some useful facts about factorization, I develop the important methods of calculating the Galois group and give a proof of the Chebotarev density theorem.