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Roughness is a relatively untouched field considering its significance to natural scientists. In this thesis mathematical techniques for measuring the roughness of signals are constructed and investigated. Both one dimensional and two dimensional signals are tackled. Applications include geological profiles and biological surfaces. Mathematical techniques include Fourier and Wavelet Transforms. / Thesis (M.Sc.)-University of Natal, Durban, 2001.

There is variation in Neandertal permanent dentition in both the size and shape of first molars. Ecogeography as well as chronology would be expected to account for at least some of the variation observed. Occlusal outlines of maxillary and mandibular first molar casts from European Neandertals, (Spy 1, Scladina 4A-4, Engis 2, l’Hortus 2, 4, 5, and 8, La Quina H5, Malarnaud 1) were generated through photostereomicroscopy and non-landmark smooth tracing methods, and occlusal areas, buccolingual breadths and mesiolingual lengths were measured by calibrated Motic 3.0MP microscope cameras. Principal component (PC) scores of elliptical Fourier harmonic descriptors were calculated using SHAPE v1.3, yielding a total of 76 and 67 PC scores for mandibular and maxillary data respectively. Of the maxillary outlines analyzed, a strong correlation exists between PC1 (58.4% of variance) and occlusal area, explaining size influence. On PC1, the smallest (Engis 2), is followed by Scladina 4A-A, Hortus 8, La Quina 5 and Spy 1. On PC2 (23% of variance), Scladina 4A-A is an outlier. On PC3 (12.6%), Hortus 8 is separated from the others whereas Scladina 4A-A is difficult to classify. PC4 accounts for 5.8% of the variance and separates Spy 1 from La Quina 5. Spy 1 appears as distinct on PC1, PC3, and PC4 while Scladina 4A-A is relatively distinct on all axes. In a cluster analysis of PC scores Spy 1 and La Quina 5 are linked by the shortest distance and joined secondarily to Hortus 8, whereas Scladina 4A-A and Engis 2 are relatively distinct from the others. Mandibular results indicate that Malarnaud is distinct on PC1 (40% of variance) and again on PC2 (27%), while La Quina 5 appears as slightly distinct on PC3 (14%), though grouped with Engis 2, while Hortus 2 and 4 group together this axis as well as PC1. PC4 (12%) again separates Malarnaud, and presents Hortus 5 as an outlier. Overall, chronology correlates better than geography to the variance observed in occlusal first molar shape in these European Neandertals, with some inconsistencies most likely due to individual biological variability. This study demonstrates a new method to compute the elliptical Fourier descriptors of molar occlusal outlines, and applies these to explain variation in these Neandertals with respect to ecogeographic and chronological situation.

International Telemetering Conference Proceedings / October 17-20, 1994 / Town & Country Hotel and Conference Center, San Diego, California / In many signal processing and telemetry applications only a portion of the Discrete Fourier Transform (DFT) of a data sequence is of interest. This paper develops an algorithm which enables computation of the FFT only over the frequency values of interest, reducing the computational complexity. As will be shown, the algorithm is also very modular which lends to efficient parallel processing implementation. This paper will begin by developing the frequency selective FFT algorithm, and conclude with a comparative analysis of the computational complexity of the algorithm with respect to the traditional FFT.

La presente Tesis de Investigación Doctoral hace un análisis sistemático, sistémico y armónico del registro del potencial evocado hasta llegar a la codificación de esta señal bioeléctrica para su uso como registro individual específico mediante código de barras. El código nervioso de una señal sensorial, cuyos detalles falta descifrar, está conformado por un conjunto de señales eléctricas que procesan las redes neurales del sistema sensorial, los núcleos subcorticales y la corteza cerebral, el cual es posible analizar y decodificar. Las señales nerviosas sensoriales representan por sí solas el medio exterior, pero sus procesos esenciales son decodificados en la corteza cerebral, donde se activa la información psíquica correspondiente, el decodificar las señales neuronales y su significado. Estas señales se procesan en redes simétricas interconectadas en tiempo real, es decir, existen diferentes formas simétricas de señales en cualquier estructura del cerebro. Tomando al cerebro humano como sistema de emisión de señales bioelectromagnéticas, se crea una interfaz con el potencial evocado, lo que permite analizar las distintas latencias y amplitudes en forma de señales neuronales bioelectromágneticas, expresadas en minivoltios y hertzios, dentro de una longitud de onda que evoca el cerebro, utilizando modelos matemáticos como las series de Fourier, wavelets y fractales. En esta interfaz se introduce el código de barras que es un código basado en la representación mediante un conjunto de líneas paralelas verticales de distinto grosor y espaciado, que en su conjunto contienen una determinada información. De este modo, el código de barras permite reconocer rápidamente a una persona, en tanto permite generar un registro individual específico de esta persona. Con esta finalidad, se obtuvieron pruebas médicas del potencial evocado y se decodificaron mediante la trasformada de Fourier, lo que permitió la descomposición de la señal en componentes de frecuencias diferentes, g, que corresponde al espectro de frecuencias de la señal f. Luego, estas fueron procesadas mediante los modelos fractales, lográndose obtener una trasformada que se expresa en un código de barras personalizado. Es decir, el código nervioso es descifrado mediante la matematización con el uso de las series de Fourier y el procesamiento de la dimensión fractal y de su transformada, hacia un código de barras con múltiples aplicaciones en todas las ciencias. / -- The following Ph.D. thesis research presents a systematic, systemic and harmonic analysis from the evoked potential record until the encoding of this bioelectric signal; in order to use it as a specific individual record through barcode. The nervous code of a sensorial signal, which details need to be decoded, is formed by a group of electrical signal that processes the neural networks of the sensorial system, the sub cortical nuclei and the cerebral cortex. It is possible to analyze and decode. The sensorial nervous signals represent themselves the external mean, but their essential process is decoded at the cerebral cortex level, where it actives the respective psychic information. To decode the neural signals and their meaning. These signals are processed in real-time interconnected symmetrical networks, which mean there are different shapes of symmetrical signals within any brain structure. Taking the human brain as a bioelectromagnetic signal emission system, an interface is created with the evoked potential, which allows analyzing the different latencies and amplitudes through bioelectromagnetic neural signals, expressed on mini volts and hertz, within a wavelength that evokes the brain using mathematical models such as the Fourier series, wavelets and fractals. In this interface, a barcode is produced, which is a code based on the representation of a group of vertical parallel lines with different widths and spacings, storing specific information. In this manner, the barcode allows to recognize a person quickly, as it allows generating a specific individual record of this person. In this way, clinical tests of the evoked potential were obtained, they were decoded by the Fourier Transform, which allowed decomposing a signal into components of different frequency, g, represents the frequency spectrum of the signal f. Then, it was processed through fractal models obtaining a transform expressed by a personal barcode. In other words, the nervous code is decoded by mathematical means, using the Fourier series and the process fractal dimension and its transform, into a barcode with multiple applications to several sciences.

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Title: Dynamic model for estimation of radon concentration in buildings Author: Barbora Vaňková Department: Department of probability and mathematical statistics Supervisor: Ing. Marek Brabec, Ph.D. Supervisor's e-mail address: mbrabec@cs.cas.cz Abstract: In the present work there is described the method for estimation of functi- onal data from discrete values and basic methods of functional data analysis. 1

Ultrasonic technology is commonly used in the eld of Non-Destructive Testing (NDT) of metal structures such as steel, aluminium, etc. Compared to ultrasonic bulk waves that travel in infinite media with no boundary influence, Ultrasonic Guided Waves (UGWs) require a structural boundary for propagation such that they can be used to inspect and monitor long elements of a structure from a single position. The greatest challenges for any UGW system are the plethora of wave modes arising from the geometry of the structural element which propagate with a range of frequency dependent velocities and the interpretation of these combined signals reflected by discontinuities in the structural element. In this thesis, a technique is developed which facilitates the measurement of Time of Arrival (ToA) and group velocity dispersion curves of wave modes for one dimensional structures as far as wave propagation is concerned. A second technique is also presented which employs the dispersion curves to deliver enhanced range measurements in complex multimodal UGW responses. Ultimately, the aforementioned techniques are used as a part of the analysis of previously unreported signals arising from interactions of UGWs with piezoelectric transducers. The first signal processing technique is presented which used a combination of frequency-sweep measurement, sampling rate conversion and the Fourier transform. The technique is applied to synthesized and experimental data in order to identify different wave modes in complex UGW signals. It is demonstrated that the technique has the capability to derive the ToA and group velocity dispersion curve of the wave modes of interest. The second signal processing technique uses broad band excitation, dispersion compensation and cross-correlation. The technique is applied to synthesized and experimental data in order to identify different wave modes in complex UGW signals. It is demonstrated that the technique noticeably improves the Signal to Noise Ratio (SNR) of the UGW response using a priori knowledge of the dispersion curve. It is also able to derive accurate quantitative information about the ToA and the propagation distance. During the development of the aforementioned signal processing techniques, some unwanted wave-packets are identified in the UGW responses which are found to be induced by the coupling of a shear mode piezoelectric transducer at the free edge of the waveguide. Accordingly, the effect of the force on the piezoelectric transducers and the corresponding reflections and mode conversions are studied experimentally. The aforementioned signal processing techniques are also employed as a part of the study. A Finite Element Analysis (FEA) procedure is also presented which can potentially improve the theoretical predictions and converge to results found in experimental routines. The approach enhances the con dence in the FEA models compared to traditional approaches. The outcome of the research conducted in this thesis paves the way to enhance the reliability of UGW inspections by utilizing the signal processing techniques and studying the multimodal responses.

The Polarizer-Sample-Analyzer (PSA) arrangement with the optical components P and A rotating with a fixed speed ratio (3:1) was originally introduced to determine nine Mueller matrix elements from Fourier analysis of the output signal of a photodetector. The arrangement is modified to the P'PSAA' arrangement where P' and A' represent fixed polarizers that are added at both ends with the speed ratio of the rotating components (P and A) remaining the same as before. After determination of the partial Mueller matrix in the ideal case, azimuthal offsets and imperfection parameters are introduced in the straight-through configuration and the imperfection parameters are determined from the Fourier coefficients. Finally, the sample is reintroduced and the full Mueller matrix elements are calculated to show the deviation from the ideal case and their dependency on the offsets and imperfection parameters.

We propose and demonstrate the superiority of using a phase SLM only in a multi-reference phase encoded joint transform correlator(JTC) compared to an ordinary JTC. Maximal length sequences are shifted to form two dimensional orthogonal arrays referred as m-arrays. The phase mask is used in one step to encode multiple reference images and at the same time eliminate false correlation peaks through power spectrum dispersion. A theoretical model of the implemented JTC is mathematically expressed and explained in this thesis. Basic performance criteria, PSR (peak to side lobe ratio) and PCE (peak to correlation energy), are used for comparative analysis, and their relationship to joint input image size and SLM size are investigated and the results simulated.