Neste texto são revisados métodos de reamostragem de séries temporais discretas baseados em wavelets, como alternativas as abordagens clássicas, feitas nos domínios do tempo e da frequência. Tais métodos, conhecidos na literatura como wavestrap e wavestrapping fazem uso, respectivamente, das transformadas wavelet discreta (DWT) e wavelet packet discreta (DWPT). Existem poucos resultados sobre a aplicação da DWPT, de forma que este texto pode ser considerado uma contribuição. Aqui mostra-se também, a superioridade do wavestrapping sobre o wavestrap quando aplicados na estimação da densidade espectral de potência de séries temporais sintéticas geradas a partir de modelos autoregressivos. Tais séries possuem uma particularidade interessante que são picos, geralmente acentuados, em sua reapresentação espectral, de tal forma que grande parte dos métodos clássicos de reamostragem apresentam resultados viesados quando aplicados a estes casos. / This paper reviews resampling methods based on wavelets as an alternative to the classic approaches which are, made in the time and frequency domains. These methods, known in the literature as wavestrap and wavestrapping, make use, respectively, of the discrete wavelet transform (DWT) and of the discrete wavelet packet transform (DWPT). Since only few results are avaliable when the DWPT is applied, this text can be considered a contribution to the subject. Here we, also show the superiority of wavestrapping over wavestrap when they are applied to the estimation of power spectral densities of the synthetic time series generated from autoregressive models. These series have an interesting feature that are sharp peaks in their spectral representation, so that most of the traditional methods of resampling lead to biased results.

Neste texto são revisados métodos de reamostragem de séries temporais discretas baseados em wavelets, como alternativas as abordagens clássicas, feitas nos domínios do tempo e da frequência. Tais métodos, conhecidos na literatura como wavestrap e wavestrapping fazem uso, respectivamente, das transformadas wavelet discreta (DWT) e wavelet packet discreta (DWPT). Existem poucos resultados sobre a aplicação da DWPT, de forma que este texto pode ser considerado uma contribuição. Aqui mostra-se também, a superioridade do wavestrapping sobre o wavestrap quando aplicados na estimação da densidade espectral de potência de séries temporais sintéticas geradas a partir de modelos autoregressivos. Tais séries possuem uma particularidade interessante que são picos, geralmente acentuados, em sua reapresentação espectral, de tal forma que grande parte dos métodos clássicos de reamostragem apresentam resultados viesados quando aplicados a estes casos. / This paper reviews resampling methods based on wavelets as an alternative to the classic approaches which are, made in the time and frequency domains. These methods, known in the literature as wavestrap and wavestrapping, make use, respectively, of the discrete wavelet transform (DWT) and of the discrete wavelet packet transform (DWPT). Since only few results are avaliable when the DWPT is applied, this text can be considered a contribution to the subject. Here we, also show the superiority of wavestrapping over wavestrap when they are applied to the estimation of power spectral densities of the synthetic time series generated from autoregressive models. These series have an interesting feature that are sharp peaks in their spectral representation, so that most of the traditional methods of resampling lead to biased results.

The problems of achieving high detection rate with low false alarm rate for human detection and tracking in video sequence, performance scalability, and improving response time are addressed in this thesis. The underlying causes are the effect of scene complexity, human-to-human interactions, scale changes, and scene background-human interactions. A two-stage processing solution, namely, human detection, and human tracking with two novel pattern classifiers is presented. Scale independent human detection is achieved by processing in the wavelet domain using square wavelet features. These features used to characterise human silhouettes at different scales are similar to rectangular features used in [Viola 2001]. At the detection stage two detectors are combined to improve detection rate. The first detector is based on shape-outline of humans extracted from the scene using a reduced complexity outline extraction algorithm. A Shape mismatch measure is used to differentiate between the human and the background class. The second detector uses rectangular features as primitives for silhouette description in the wavelet domain. The marginal distribution of features collocated at a particular position on a candidate human (a patch of the image) is used to describe statistically the silhouette. Two similarity measures are computed between a candidate human and the model histograms of human and non human classes. The similarity measure is used to discriminate between the human and the non human class. At the tracking stage, a tracker based on joint probabilistic data association filter (JPDAF) for data association, and motion correspondence is presented. Track clustering is used to reduce hypothesis enumeration complexity. Towards improving response time with increase in frame dimension, scene complexity, and number of channels; a scalable algorithmic architecture and operating accuracy prediction technique is presented. A scheduling strategy for improving the response time and throughput by parallel processing is also presented.

This study introduces new families of wavelets. The first is directly derived from the response of Second Order Underdamped Linear-Time-Invariant (SOULTI) systems, while the second is a generalization of the first to the complex domain and is similar to the Laplace transform kernel function. The first takes the acronym of SOULTI wavelet, while the second is named the Laplace wavelet. The most important criteria for a function or signal to be a wavelet is the ability to recover the original signal back from its continuous wavelet transform. It is shown that it is possible to recover back the original signal once the SOULTI or the Laplace wavelet transform is applied to decompose the signal. It is found that both wavelet transforms satisfy linear differential equations called the reconstructing differential equations, which are closely related to the differential equations that produce the wavelets. The new wavelets can have well defined Time-Frequency resolutions, and they have useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying harmonic signals, and linear relations between the wavelet transform of signals and the wavelet transform of their derivatives and integrals. The defined wavelets are applied to system analysis applications. The new wavelets showed accurate instantaneous frequency identification and modal decomposition of LTI Multi-Degree of Freedom (MDOF) systems and it showed better results than the Short-time Fourier Transform (STFT) and the other harmonic wavelets used in time-frequency analysis. The modal decomposition is applied for modal parameters identification, and the properties of the Laplace and the SOULTI wavelet transforms allows analytical and accurate identification methods. / Ph. D. / This study introduces new families of wavelets (small wave-like functions) derived from the response of Second Order Underdamped (oscillating) Linear-Time-Invariant systems. The first is named the SOULTI wavelets, while the second is named Laplace Wavelets. These functions can be used in a wavelet transform which transfers signals from the time domain to the time-frequency domain. It is shown that it is possible to recover back the original signal once the transform is applied. The new wavelets can have well defined Time-Frequency resolutions. The time-frequency resolution is the multiplication of the time resolution and the frequency resolution. A resolution is the smallest time range or frequency range that carries a feature of the signal. The new wavelets have useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying oscillating signals, and linear relations between the wavelet transform of signals and the wavelet transform of their derivatives and integrals. The defined wavelets are applied to system analysis applications. The new wavelets showed accurate instantaneous frequency identification, and decomposing signals into the basic oscillation frequencies, called the modes of vibration. In addition, the new wavelets are applied to infer the parameters of dynamic systems, and they show better results than the Short-time Fourier Transform (STFT) and the other wavelets used in time-frequency analysis.