In this thesis, the radar pulse repetition interval (PRI) tracking with Kalman Filter problem is investigated. The most common types of PRIs are constant PRI, step (jittered) PRI, staggered PRI, sinusoidally modulated PRI. This thesis considers the step (this type of PRI agility is called as constant PRI when the jitter on PRI values is eliminated) and staggered PRI cases. Different algorithms have been developed for tracking step and staggered PRIs cases. Some useful simplifications are obtained in the algorithm developed for step PRI sequence. Two different algorithms robust to the effects of missing pulses obtained for staggered PRI sequence are compared according to estimation performances. Both algorithms have two parts: detection of the period part and a Kalman filter model. The advantages and disadvantages of these algorithms are presented. Simulations are implemented in MATLAB.

Speech has been the subject of interest for a very long time. Even with so much advancement in the processing techniques and in the understanding of the source of speech, it is, even today, rather difficult to generate speech in the laboratory in all its aspects. A simple aspect like how the speech can retain its intelligibility even if it is distorted or band passed is not really understood. This thesis deals with one small feature of speech viz., the intelligibility of speech is retained even when it is bandpassed with a minimum bandwidth of around 1 KHz located any where on the speech spectrum of 0-4 KHz. Several experiments have been conducted by the earlier workers by passing speech through various distortors like differentiators, integrators and infinite peak clippers and it is found that the intelligibility is retained to a very large extent in the distorted speech. The integrator and the differentiator remove essentially a certain portion of the spectrum. Therefore, it is thought that the intelligibility of the speech is spread over the entire speech spectrum and that, the intelligibility of speech may not be impaired even when it is bandpassed with a minimum bandwidth and the band may be located any where in the speech spectrum. To test this idea and establish this feature if it exists, preliminary experiments have been conducted by passing the speech through different filters and it is found that the conjecture seems to be on the right line. To carry out systematic experiments on this an experimental set up has been designed and fabricated which consists of a microprocessor controlled speech recording, storing and speech playback system. Also, a personal computer is coupled to the microprocessor system to enable the storage and processing of the data. Thirty persons drawn from different walks of life like teachers, mechanics and students have been involved for collecting the samples and for recognition of the information of the processed speech. Even though the sentences like 'This is devices lab' are used to ascertain the effect of bandwidth on the intelligibility, for the purpose of analysis, vowels are used as the speech samples. The experiments essentially consist of recording words and sentences spoken by the 30 participants and these recorded speech samples are passed through different filters with different bandwidths and central frequencies. The filtered output is played back to the various listeners and observations regarding the intelligibility of the speech are noted. The listeners do not have any prior information about the content of the speech. It has been found that in almost all (95%) cases, the messages or words are intelligible for most of the listeners when the band width of the filter is about 1 KHz and this is independent of the location of the pass band in the spectrum of 0-4 KHz. To understand how this feature of speech arises, spectrums of vowels spoken by 30 people have using FFT algorithms on the digitized samples of the speech. It is felt that there is a cyclic behavior of the spectrum in all the samples. To make sure that the periodicity is present and also to arrive at the periodicity, a moving average procedure is employed to smoothen the spectrum. The smoothened spectrums of all the vowels indeed show a periodicity of about 1 KHz. When the periodicities are analysed the average value of the periodicities has been found to be 1038 Hz with a standard deviation of 19 Hz. In view of this it is thought that the acoustic source responsible for speech must have generated this periodic spectrum, which might have been modified periodically to imprint the intelligibility. If this is true, one can perhaps easily understand this feature of the speech viz., the intelligibility is retained in a bandpassed speech of bandwidth 1 K H z . the pass band located any where in the speech spectrum of 0-4 KHz. This thesis describing the experiments and the analysis of the speech has been presented in 5 chapters. Chapter 1 deals with the basics of speech and the processing tools used to analyse the speech signal. Chapter 2 presents the literature survey from where the present problem is tracked down. Chapter 3 describes the details of the structure and the fabrication of the experimental setup that has been used. In chapter 4, the detailed account of the way in which the experiments are conducted and the way in which the speech is analysed is given. In conclusion in chapter 5, the work is summarised and the future work needed to establish the mechanism of speech responsible for the feature of speech described in this thesis is suggested.

In cryptography, periodic sequences with terms in F2 are used almost everywhere. These sequences should have large linear complexity to be cryptographically strong. In fact, the linear complexity of a sequence should be close to its period. In this thesis, we study the expected value for N-periodic sequences with terms in the finite field Fq. This study is entirely devoted to W. Meidl and Harald Niederreiter&rsquo / s paper which is &ldquo / On the Expected Value of the Linear Complexity and the k-Error Linear Complexity of Periodic Sequences&rdquo / We only expand this paper, there is no improvement. In this paper there are important theorems and results about the expected value of linear complexity of periodic sequences.

This work deals with the further development of a method for Direction of Arrival (DOA) estimation based on the Discrete Fourier Transform (DFT) of the sensor array output. In the existing DFT-based algorithm, relatively high SNR is considered, and it is assumed that a large number of sensors are available. In this study an overview of some of the most commonly used DOA estimation techniques will be presented. Then the performance of the DFT method will be analyzed and compared with the performance of existing techniques. Two main objectives will be studied, firstly the reduction of the number of sensors and secondly the performance of the DFT based technique in the presence of noise. Experimental simulations will be presented to illustrate that in absence of noise, the proposed method is very fast and using just one snapshot is sufficient to accurately estimate DOAs. Also, in presence of noise, the method is still relatively fast and using a small number of snapshots, it can accurately estimate DOAs. The above mentioned properties are the result of taking an average of the peaks of the DFTs, X_n (k), obtained from a sequence of N_s snapshots. With N_s sufficiently large, the average over N_s snapshots approaches expected value. Also, the conditions that should be satisfied to avoid overlapping of main-lobes, and thus loosing the DOA of some signals, in the DFT spectrum are examined. This study further analyzes the performance of the proposed method as well as two other commonly used algorithms, MUSIC and conventional beamformer. An extensive simulation was conducted and different features of the spatial DFT technique, such as accuracy, resolution, sensitivity to noise, effect of multiple snapshots and the number of sensors were evaluated and compared with those of existing techniques. The simulations indicate that in most aspects the proposed spatial DFT algorithm outperforms the other techniques. / Graduate

Made available in DSpace on 2014-06-11T19:22:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-08-28Bitstream added on 2014-06-13T18:08:26Z : No. of bitstreams: 1 matos_er_me_ilha.pdf: 2466056 bytes, checksum: fd089ec7147abd26c94fadfe5e17bb85 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho apresenta-se uma Metodologia para Detecção e Classificação de Curtos-Circuitos em alimentadores de Sistemas de Distribuição de Energia Elétrica fundamentada na análise de registros oscilográficos através da DFT (Discrete Fourier Transform) e de RNAs (Redes Neurais Artificiais). Sua aplicação pressupõe a disponibilidade de registros de oscilografia digital das correntes nas três fases do alimentador, monitoradas apenas na saída da subestação. A caracterização de cada tipo de curto-circuito é obtida mediante a análise do comportamento dinâmico das correntes de fase durante o período transitório das faltas e a detecção e classificação dos curtos-circuitos são efetuadas por meio de um banco de RNAs acíclicas, do tipo perceptrons, de múltiplas camadas. Um modelo de um alimentador real de Sistema de Distribuição de grande porte, composto por 836 barras, foi utilizado na obtenção dos dados referentes aos curtos-circuitos, com simulações via software ATP-EMTP (Alternative Transients Program - Electromagnetic Transients Program). O método foi implementado e testado utilizando-se o software MATLAB®. Como resultado tem-se uma metodologia de formulação simples que apresenta bom desempenho, é de fácil implementação, apresenta baixa carga computacional e gera resultados altamente satisfatórios / This work proposes a methodology for Detection and Classification of Short-Circuits in Distribution Electric Power feeders, based on the analysis of oscillograph records through the application of DFT (Discrete Fourier Transform) and ANNs (Artificial Neural Networks). Its application requires the availability of digital oscillograph records of the currents in the three phases of the feeder, only monitored at the output of the substation. The characterization of each type of short-circuit is obtained by means of analysis of the dynamic behavior of the phase currents during the transitory period. The detection and classification of short-circuits is performed by a bank of acyclic ANNs, of type multilayers perceptrons. A real feeder model of a large distribution power system, composed of 836 buses, was used to obtain data relating to short-circuits, simulated via ATP-EMTP (Alternative Transients Program - Electromagnetic Transients Program) software. The method was implemented and tested using MATLAB®. As a conclusion, the proposed method is simple to be implemented, presents low computational load and generates good results

Táto diplomová práca sa zaoberá návrhom a implementáciou algoritmu pre spracovaniu signálu z radaru využívajúceho frekvenčne modulovanú kontinuálnu vlnu. Cieľom je implementácia algoritmu, ktorý by bol dostatočne rýchly (výpočet v reálnom čase na cieľovej platforme) a dostatočne presný pre použitie v rádiovýškomere v ľahkom lietadle so zameraním na použitie počas pristávacieho manévru. Hlavnou metódou spracovania signálu, použitou v implementácii, je Diskrétna Fourierova transformácia. Vytvorený algoritmus bol otestovaný na reálnych letových dátach a pre pristávací manéver dosiahol uspokojivé výsledky.

The master's thesis is concerned with digital image denoising methods. The theoretical part explains some elementary terms related to image processing, image noise, categorization of noise and quality determining criteria of denoising process. There are also particular denoising methods described, mentioning their advantages and disadvantages in this paper. The practical part deals with an implementation of the selected denoising methods in a Java, in the environment of application RapidMiner. In conclusion, the results obtained by different methods are compared.

The Discrete Fourier Transform (DFT) and its improved formulations, the Fast Fourier Transforms (FFTs), are vital for scientists and engineers in a range of domains from signal processing to the solution of partial differential equations.  A growing trend in Scientific Computing is heterogeneous computing, where accelerators are used instead or together with CPUs. This has led to problems for developers in unifying portability, performance, and productivity.  This thesis first motivates this work by showing the importance of having efficient DFT calculations, describes the DFT algorithm and a formulation based on matrix-factorizations which has been developed to formulate FFT algorithms and express their parallelism to exploit modern computer architectures, such as accelerators. The first paper is a motivating study of the breakdown of the performance and scalability of the high-performance Molecular Dynamics code GROMACS where DFT calculations are a main performance bottleneck. In particular, the long-range interactions are solved with the Particle-Mesh Ewald algorithm which uses a three-dimensional Fast Fourier Transform.  The two following papers present two approaches to leverage factorization with the help of two different frameworks using Intermediate Representation and compiler technology, for the development of fast and portable code. The second paper presents a front-end and a pipeline for code generation in a domain-specific language based on Multi-Level Intermediate Representation (MLIR) for developing Fast Fourier Transform libraries. The last paper investigates and optimizes an implementation of an important kernel within the matrix-factorization framework: the batched DFT. It is implemented with data-centric programming and a data-centric intermediate representation called Stateful Dataflow multi-graphs (SDFG). The paper evaluates strategies for complex-valued data layout for performance and portability and we show that there is a trade-off between portability and maintainability in using the native complex data type and that an SDFG-level abstraction could be beneficial for developing higher-level applications. / Den diskreta Fouriertransformen och dess snabba implementeringar är viktiga för vetenskap och ingenjörskonst. Den har tillämningar i ämnen som singnal behnadling, lösning av partiella diffrentialekvationer och många andra ämnen inom vetenskapliga beräkningar. En växande trend inom ämnet är heterogena datorer där acceleratorer som är specialicerade till vissa beräkningar kan användas som stöd för traditionella processorer. Detta leder till problem med portabilitet, prestanda och produktivitet.  Avhandligen inleds med att beskriva diskret Fouriertransform och ett ramverk för faktorisering till glesa strukturerade matriser som tillsammans representerar snabb Fouriertransform (FFT, Eng.) och som kan användas för att uttrycka parallelism i algorithmerna. För att motivera arbete med FFT i vetenskapliga beräkningar så utväreras den parallela prestandan av GROMACS: en kod för simulering av Molekyldynmik. GROMACS använder en tredimensionell diskret Fouriertransform för att finna den elektrostatiska potentialen med hjälp av Particle-Mesh Ewald-tekniken.  De följande två artiklarna presenterar två olika ramverk för att utnyttja mellankod (IR Eng.) och kompilatorteknik, för utvecklandet av  snabb och portabel kod. Den andra artikeln beskriver arbetet att utveckla ett domänspecifikt språk baserat på Multi-Level Intermediate Representation för design av snabba Fouriertransformer baserat på matrisfaktorisering. Den sista artikeln undersöker och optimerar en viktig komponent för matrisfaktorisering av diskreta Fouriertransformen: att beräkna flera små diskreta Fouriertransformer parallelt. Detta är gjort med DaCe som är ramverk för data-centrisk programmering som använder en mellankod kallad SDFG. I artikeln utvärderas strategier för data format av komplexa tal för prestanda och portabilitet, och visar att en abstraktion med hjälp av SDFG kan motiveras. / <p>QC 20230522</p>

We provide a Frequentist-Bayesian hybrid test statistic in this dissertation for two testing problems. The first one is to design a test for the significant differences between non-parametric functions and the second one is to design a test allowing any departure of predictors of high dimensional X from constant. The implementation is also given in construction of the proposal test statistics for both problems. For the first testing problem, we consider the statistical difference among massive outcomes or signals to be of interest in many diverse fields including neurophysiology, imaging, engineering, and other related fields. However, such data often have nonlinear system, including to row/column patterns, having non-normal distribution, and other hard-to-identifying internal relationship, which lead to difficulties in testing the significance in difference between them for both unknown relationship and high-dimensionality. In this dissertation, we propose an Adaptive Bayes Sum Test capable of testing the significance between two nonlinear system basing on universal non-parametric mathematical decomposition/smoothing components. Our approach is developed from adapting the Bayes sum test statistic by Hart (2009). Any internal pattern is treated through Fourier transformation. Resampling techniques are applied to construct the empirical distribution of test statistic to reduce the effect of non-normal distribution. A simulation study suggests our approach performs better than the alternative method, the Adaptive Neyman Test by Fan and Lin (1998). The usefulness of our approach is demonstrated with an application in the identification of electronic chips as well as an application to test the change of pattern of precipitations. For the second testing problem, currently numerous statistical methods have been developed for analyzing high-dimensional data. These methods mainly focus on variable selection approach, but are limited for purpose of testing with high-dimensional data, and often are required to have explicit derivative likelihood functions. In this dissertation, we propose ``Hybrid Omnibus Test'' for high-dimensional data testing purpose with much less requirements. Our Hybrid Omnibus Test is developed under semi-parametric framework where likelihood function is no longer necessary. Our Hybrid Omnibus Test is a version of Freqentist-Bayesian hybrid score-type test for a functional generalized partial linear single index model, which has link being functional of predictors through a generalized partially linear single index. We propose an efficient score based on estimating equation to the mathematical difficulty in likelihood derivation and construct our Hybrid Omnibus Test. We compare our approach with a empirical likelihood ratio test and Bayesian inference based on Bayes factor using simulation study in terms of false positive rate and true positive rate. Our simulation results suggest that our approach outperforms in terms of false positive rate, true positive rate, and computation cost in high-dimensional case and low-dimensional case. The advantage of our approach is also demonstrated by published biological results with application to a genetic pathway data of type II diabetes. / Ph. D.

This thesis concerns the mathematics and application of various methods for approximating matrices, with a particular eye towards the role that such methods play in image compression. An image is stored as a matrix of values with each entry containing a value recording the intensity of a corresponding pixel, so image compression is essentially equivalent to matrix approximation. First, we look at the singular value decomposition, one of the central tools for analyzing a matrix. We show that, in a sense, the singular value decomposition is the best low-rank approximation of any matrix. However, the singular value decomposition has some serious shortcomings as an approximation method in the context of digital images. The second method we consider is the discrete Fourier transform, which does not require the storage of basis vectors (unlike the SVD). We describe the fast Fourier transform, which is a remarkably efficient method for computing the discrete cosine transform, and how we can use this method to reduce the information in a matrix. Finally, we look at the discrete cosine transform, which reduces the complexity of the calculation further by restricting to a real basis. We also look at how we can apply a filter to adjust the relative importance of the data encoded by the discrete cosine transform prior to compression. In addition, we developed code implementing the ideas explored in the thesis and demonstrating examples.