Orientadores: Furio Damiani, Romis Ribeiro de Faissol Attux / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-27T01:42:11Z (GMT). No. of bitstreams: 1 FernandesJunior_AntonioCarlosLopes_D.pdf: 3251957 bytes, checksum: 7a047b751489da833ab7c5efd9cd86ee (MD5) Previous issue date: 2015 / Resumo: A deteção de tempo em um sinal musical é uma tarefa muito importante em diversas aplicações. A presente tese apresenta os resultados da detecção de andamento usando uma nova abordagem baseada na extração de atributos de um conjunto de funções de detecção de periodicidade e aprendizado de máquina. Para isto a transformada wavelet foi utilizada para separar o sinal musical em diferentes resoluções e o domínio complexo retificado foi aplicado para a construção de funções de deteccão de onsets. Em seguida, as funções de deteccão de periodicidade para cada nível wavelet foram geradas por operações de autocorrelação. Descritores de áudio clássicos foram adaptados e extraídos de cada função de periodicidade e foram usados como entradas para a máquina de aprendizado que mapeia os descritores para o tempo da música. As máquinas utilizadas foram o perceptron de múltiplas camadas e a máquina de aprendizado extremo, com propostas diferenciadas de configuração. Um método para classificação e avaliação dos descritores foi proposto. Também, neste trabalho, um novo descritor foi proposto. Um método de seleção forward de atributos via Gram-Schmidt foi aplicado para a escolha do melhor subconjunto para o treinamento da máquina. Foi ainda aplicado um método de clustering via K-means para a partilha de observações entre os conjuntos de treinamento, teste e validação, e foi proposto um novo método de seleção de observações via análise de componentes principais denominado de seleção esférica de observações / Abstract: Tempo detection in a music signal is a very important task for many applications. This thesis presents results concerning this task using a new approach based on the extraction of features from a set of periodicity detection functions and on machine learning. The wavelet transform was utilized to separate the musical signal at different resolutions and the rectified complex domain was applied to the construction of onset detection functions. Then, periodicity detection functions for each resolution were generated by autocorrelation operations. Classic audio features were extracted from each periodicity function and were used as inputs to a neural network that maps descriptors to music tempo. The used machines were the multilayer perceptron and an extreme learning machine, with different configuration proposals. A method for classification and evaluation of features has been proposed. Also, in this work, a new descriptor has been proposed. A method of forward selection via Gram-Schmidt was applied to choosing the best subset for the machine training. A K-means clustering method was also applied for partitioning observations between the training sets and a new observation selection method via principal component analysis, called spherical selection of observations, was proposed / Doutorado / Eletrônica, Microeletrônica e Optoeletrônica / Doutor em Engenharia Elétrica

In this thesis, we establish the underlying research background necessary for tackling the problem of phase-shifting in the wavelet transform domain. Solving this problem is the key to reducing the redundancy and huge storage requirement in Image-Based Rendering (IBR) applications, which utilize wavelets. Image-based methods for rendering of dynamic glossy objects do not truly scale to all possible frequencies and high sampling rates without trading storage, glossiness, or computational time, while varying both lighting and viewpoint. This is due to the fact that current approaches are limited to precomputed radiance transfer (PRT), which is prohibitively expensive in terms of memory requirements when both lighting and viewpoint variation are required together with high sampling rates for high frequency lighting of glossy material. At the root of the above problem is the lack of a closed-form run-time solution to the nontrivial problem of rotating wavelets, which we solve in this thesis. We specifically target Haar wavelets, which provide the most efficient solution to solving the tripleproduct integral, which in turn is fundamental to solving the environment lighting problem. The problem is divided into three main steps, each of which provides several key theoretical contributions. First, we derive closed-form expressions for linear phase-shifting in the Haar domain for one-dimensional signals, which can be generalized to N-dimensional signals due to separability. Second, we derive closed-form expressions for linear phase-shifting for two-dimensional signals that are projected using the non-separable Haar transform. For both cases, we show that the coefficients of the shifted data can be computed solely by using the coefficients of the original data. We also derive closed-form expressions for non-integer shifts, which has not been reported before. As an application example of these results, we apply the new formulae to image shifting, rotation and interpolation, and demonstrate the superiority of the proposed solutions to existing methods. In the third step, we establish a solution for non-linear phase-shifting of two-dimensional non-separable Haar-transformed signals, which is directly applicable to the original problem of image-based rendering. Our solution is the first attempt to provide an analytic solution to the difficult problem of rotating wavelets in the transform domain.

Wavlet analysis and its advantages in determining time-varying characteristics are discussed. The Morlet wavelet is defined and procedures for choosing its parameters are described. The recovery of modulation characteristics using the Morlet wavelet is demonstrated. Hydrodynamic linear stability is reviewed and its application to steady and unsteady mixing layers is discussed. Modulation effects are demonstrated by using the magnitude and phase of the wavelet coefficients. The time-varying characteristics of the most unstable modes are determined using the real part of the wavelet coefficients. It is found that mean flow unsteadiness increases the amplitude and phase modulation of the mixing layers. Synchronized variations of the two most unstable modes, the fundamental and the subharmonic, are also observed in the region of subharmonic growth. In a second application of wavelet analysis, the phase lag of the wavelet coefficients is used to determine the phase relation between the fundamental and the subharmonic in acoustically forced mixing layers. The results show that selective forcing affects the time-variations of the phase relation. In a third application, the magnitude and phase of the wavelet coefficients are used to decompose propagating waves measured at a single location. / Master of Science

Thesis (DSc (Mathematical Sciences))--University of Stellenbosch, 2005. / Subdivision is an important iterative technique for the efficient generation of curves and surfaces in geometric modelling. The convergence of a subdivision scheme is closely connected to the existence of a corresponding refinable function. In turn, such a refinable function can be used in the multi-resolutional construction method for wavelets, which are applied in many areas of signal analysis.

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy

The properties and imaging performance of the computed tomographicimaging spectrometer (CTIS) have been investigated with Fourierand wavelet crosstalk matrices. These matrices and theircorresponding datacube reconstruction algorithms explicitly usedsensitivity equations describing the CTIS imaging system. Theseequations derived from Franhofer diffraction theory of thecomputed generated hologram (CGH) disperser, serve as themathematical model of the CTIS.The Fourier crosstalk matrix (FCTM) was primarily used to analyzethe CTIS imaging system. The FCTM describes which spatial andspectral frequencies contribute to object cube data entering thesystem and whether or not these frequencies give distinctcontributions with respect to each other. Furthermore, since theCTIS is a limited angle tomographic imaging system the missingcone of frequencies which is a feature of this instrument isclearly shown using the FCTM. Subsequently, Fourier-basedestimates of the reconstructed object cube (i.e. the datacube)will be missing this frequency information even if the CTIS is aperfect optical system.The wavelet crosstalk matrix (WCTM) was used primarily for efficient datacubereconstruction only. The datacube reconstruction calculations areprimarily proof-of-concept and reproduce the Fourier results withsome absence of Fourier related artifacts. The waveletdecomposition of the object cube is useful for studying multipleobjects in a parallel processing environment withoutreconstructing the entire datacube, thus reducing overall complexity.Datacube reconstructions of actual astronomical observations withthe CTIS, using the techniques of this research, were consistentwith previous independent datacube estimates from the same datausing existing conventional techniques. Furthermore these objectsfurnish natural point-spread functions that supplementcomputational simulations of the CTIS by describing actual imagingsystem performance.The computational tools for the study ofthe CTIS imaging system provide the additional bonus of ananalysis of object detectability by the computation of receiveroperator characteristic (ROC) curves. We used a synthetic binarystar to simulate this in the presence of both detector and objectnoise.Some suggestions for future research directions are given.

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.

Over the past few decades, the demand for digital information has increased drastically. This enormous demand poses serious difficulties on the storage and transmission bandwidth of the current technologies. One possible solution to overcome this approach is to compress the amount of information by discarding all the redundancies. In multimedia technology, various lossy compression techniques are used to compress the raw image data to facilitate storage and to fit the transmission bandwidth. In this thesis, we propose a new approach using algebraic integers to reduce the complexity of the Daubechies-4 (D4) and Daubechies-6 (D6) Lifting based Discrete Wavelet Transforms. The resulting architecture is completely integer based, which is free from the round-off error that is caused in floating point calculations. The filter coefficients of the two transforms of Daubechies family are individually converted to integers by multiplying it with value of 2x, where, x is a random value selected at a point where the quantity of losses is negligible. The wavelet coefficients are then quantized using the proposed iterative individual-subband coding algorithm. The proposed coding algorithm is adopted from the well-known Embedded Zerotree Wavelet (EZW) coding. The results obtained from simulation shows that the proposed coding algorithm proves to be much faster than its predecessor, and at the same time, produces good Peak Signal to Noise Ratio (PSNR) at very low bit rates. Finally, the two proposed transform architectures are implemented on Virtex-E Field Programmable Gate Array (FPGA) to test the hardware cost (in terms of multipliers, adders and registers) and throughput rate. From the synthesis results, we see that the proposed algorithm has low hardware cost and a high throughput rate.