Digital Signal Processing has been dominated by the Fourier transform since the Fast Fourier Transform (FFT) was developed in 1965 by Cooley and Tukey. In the 1980's a new transform was developed called the wavelet transform, even though the first wavelet goes back to 1910. With the Fourier transform, all information about localized changes in signal features are spread out across the entire signal space, making local features global in scope. Wavelets are able to retain localized information about the signal by applying a function of a limited duration, also called a wavelet, to the signal. As with the Fourier transform, the discrete wavelet transform has an inverse transform, which allows us to make changes in a signal in the wavelet domain and then transform it back in the time domain. In this thesis, we have investigated the filtering properties of this technique and analyzed its performance under various settings. Another popular application of wavelet transform is data compression, such as described in the JPEG 2000 standard and compressed digital storage of fingerprints developed by the FBI. Previous work on filtering has focused on the discrete wavelet transform. Here, we extended that method to the stationary wavelet transform and found that it gives a performance boost of as much as 9 dB over that of the discrete wavelet transform. We also found that the SNR of noise filtering decreases as a frequency of the base signal increases up to the Nyquist limit for both the discrete and stationary wavelet transforms. Besides filtering the signal, the discrete wavelet transform can also be used to estimate the standard deviation of the white noise present in the signal. We extended the developed estimator for the discrete wavelet transform to the stationary wavelet transform. As with filtering, it is found that the quality of the estimate decreases as the frequency of the base signal increases. Many interesting signals are self-similar, which means that one of their properties is invariant on many different scales. One popular example is strict self-similarity, where an exact copy of a signal is replicated on many scales, but the most common property is statistical self-similarity, where a random segment of a signal is replicated on many different scales. In this work, we investigated wavelet-based methods to detect statistical self-similarities in a signal and their performance on various types of self-similar signals. Specifically, we found that the quality of the estimate depends on the type of the units of the signal being investigated for low Hurst exponent and on the type of edge padding being used for high Hurst exponent. / Master of Science

This thesis aims to investigate the use of the discrete wavelet transform of a stock index as a means to forecast intraday returns. This will be done by having the discrete wavelet transform as an input in a Transformers neural network with binary labels signifying a positive or negative next-day return. The input will be limited to a time horizon of 30 days since the entire history is likely not necessary, meaning we do not care about the discrete wavelet transform 5 years ago when we are trying to predict the next day's return. The network will be evaluated in terms of accuracy and a "trading strategy" on the OMXS30 index, where we compare the performance of the network with that of the original index. Overall, the performance of the discrete wavelet transform and the Transformers network was okay. The performance was slightly better than simply going long on the index, but not by much, and when factoring in transaction costs it is probably not a worthwhile strategy to use this setup. / Detta examensarbete syftar till att undersöka användningen av den diskreta wavelet-transformen av ett aktieindex som ett sätt att prognostisera nästa dags avkastning. Detta kommer att göras genom att ha den diskreta wavelet-transformen som en input i ett Transformersnätverk med målet att utföra binär klassificiering. Inputen kommer att vara begränsad till en tidshorisont på 30 dagar eftersom hela historien sannolikt inte är nödvändigt, vilket betyder att vi inte bryr oss om den diskreta wavelet-transformen för 5 år sedan när vi försöker prognostisera nästa dags avkastning. Nätverket kommer att utvärderas med hjälp av accuracy och en tradingstrategi som kommer utvärderas på OMXS30-indecet, där vi jämför tradingstrategins prestation med det ursprungliga indexet. Slutsatsen man kan dra av det här examensarbetet är att den diskreta wavelet-transformen och Transformers-nätverkets prestanda var acceptabel. Trading strategin var något bättre än att bara gå lång på indexet, men inte mycket, och när man räknar in transaktionskostnader är det förmodligen inte en lönsam strategi.

Nowadays islanding has become a big issue with the increasing use of distributed generators in power system. In order to effectively detect islanding after DG disconnects from main source, author first studied two passive islanding methods in this thesis: THD&VU method and wavelet-transform method. Compared with other passive methods, each of them has small non-detection zone, but both of them are based on the threshold limit, which is very hard to set. What’s more, when these two methods were applied to practical signals distorted with noise, they performed worse than anticipated. Thus, a new composite intelligent based method is presented in this thesis to solve the drawbacks above. The proposed method first uses wavelet-transform to detect the occurrence of events (including islanding and non-islanding) due to its sensitivity of sudden change. Then this approach utilizes artificial neural network (ANN) to classify islanding and non-islanding events. In this process, three features based on THD&VU are extracted as the input of ANN classifier. The performance of proposed method was tested on two typical distribution networks. The obtained results of two cases indicated the developed method can effectively detect islanding with low misclassification.

This thesis studies the application of the wavelet filter bank (WFB) in perceptual audio coding by providing brief overviews of perceptual coding, psychoacoustics, wavelet theory, and existing wavelet coding algorithms. Furthermore, it describes the poor frequency localization property of the WFB and explores one filter design method, in particular, for improving channel separation between the wavelet bands. A wavelet audio coder has also been developed by the author to test the new filters. Preliminary tests indicate that the new filters provide some improvement over other wavelet filters when coding audio signals that are stationary-like and contain only a few harmonic components, and similar results for other types of audio signals that contain many spectral and temporal components. It has been found that the WFB provides a flexible decomposition scheme through the choice of the tree structure and basis filter, but at the cost of poor localization properties. This flexibility can be a benefit in the context of audio coding but the poor localization properties represent a drawback. Determining ways to fully utilize this flexibility, while minimizing the effects of poor time-frequency localization, is an area that is still very much open for research.

Current transformer saturation will cause the secondary current distortion. When saturation occurs, the secondary current will not be linearly proportional to the primary current, which may lead to maloperation of protection devices. This thesis researches and tests two detecting methods: Fast Fourier Transform (FFT) and Wavelet Transform based methods. Comparing these two methods, FFT has a better performance in steady state saturation, and Wavelet Transform can determine singularity to provide the moment of distortion. The Jiles-Atherton (J-A) theory of ferromagnetic hysteresis is one approach used in electromagnetics transient modeling. With decades of development, the J-A model has evolved into different versions. The author summarizes the different models and implements J-A model in both MATLAB and Simulink.

Prematurity, especially if extreme, is one of the leading causes of problems and/or death after delivery. Among all the problems encountered by premature infants, feeding difficulties are very common. Many premature infants are fed intravenously at first, and they progress to milk feedings provided by a tube passed into the stomach. At around 34 weeks of gestation, premature infants should be able to breastfeed or take a bottle. At the same time such premature infants are usually faced with difficulty making the transition from tube-feeding to full oral feeding. In this study three physiological measurements of premature infants including sucking, swallowing and breathing were measured. The objective of this work was to detect, identify and classify these three signals independently and in relation to each other. The goal was to look at the specification of sucking, swallowing and breathing signals to extract the ratio of suck swallow-breath coordination. The results of this study were used to predict the readiness of a premature infant for introduction to oral feeding.To accomplish this, three different methods were examined. In the first method, the integration of the wavelet packet transform and a neural network was investigated. According to results of the first approach, integration of the wavelet packet transform and the neural network failed due to the inefficiency of the feature extraction method. Thus, the wavelet packet energy nodes did not provide a good feature extraction tool in this specific application.In the second approach, the frequency content of each signal was investigated to study the relationship between the shape of each waveform and the frequency content of that specific signal. Spectral analysis for suck, swallow and breathing signals showed that the shape of the signal was not tightly related to the frequency content of that specific waveform. Therefore, the frequency content could not be used as a method of feature extraction in this specific application.In the third method, the integration of correlation and matched filtering techniques was investigated and demonstrated promising result for the detection of suck and breathing signal but not for the swallowing waveform. Based on the results for sucking and breathing signals, this method should also work for good quality swallowing signal. To understand the relationship between the suck, swallow and breathing signals a matrix containing information on the time of occurrence of each event was developed.

Kernicterus causes damage to the auditory system and the basal ganglia in humans. Although the Gunn rat model of kernicterus has been extensively used to characterize the auditory features, this model has not been utilized to systematically investigate the movement disorder. In the present study, spontaneously jaundiced (jj) 16 day old Gunn rat pups were treated with sulfadimethoxine to exacerbate bilirubin neurotoxicity and compared to saline treated jjs and non-jaundiced (Nj) littermates. Electromyographic (EMG) activity was recorded from antagonistic hip muscles in dystonic and in normal appearing rats. Raw EMG signals were decomposed using the Discrete Wavelet Transform based multi-resolution analysis, and signal coefficients corresponding to the dominant EMG frequency band were chosen. Gunn rats exposed to sulfadimethoxine developed a stable clinical state characterized by prolonged abnormal axial and appendicular postures. Coherence plots revealed 4-7 Hz co-activation in antagonistic muscles that was significantly more prominent in jj sulfa treated dystonic compared to normal rats. The EMG findings support the presence of dystonia in sulfadimethoxine exposed jj Gunn rats.

Approved for public release; distribution in unlimited. / Different sensors exploit different regions of the electromagnetic spectrum; therefore, a multi-sensor image fusion system can take full advantage of the complementary capabilities of individual sensors in the suit; to produce information that cannot be obtained by viewing the images separately. In this thesis, a framework for the multiresolution fusion of the night vision devices and thermal infrared imagery is presented. It encompasses a wavelet-based approach that supports both pixel-level and region-based fusion, and aims to maximize scene content by incorporating spectral information from both the source images. In pixel-level fusion, source images are decomposed into different scales, and salient directional features are extracted and selectively fused together by comparing the corresponding wavelet coefficients. To increase the degree of subject relevance in the fusion process, a region-based approach which uses a multiresolution segmentation algorithm to partition the image domain at different scales is proposed. The region's characteristics are then determined and used to guide the fusion process. The experimental results obtained demonstrate the feasibility of the approach. Potential applications of this development include improvements in night piloting (navigation and target discrimination), law enforcement etc. / Civilian, Republic of Singapore

The thesis deals with a brief compilation of the theory of Fourier transform, linear filtration and a triad of wavelet transforms -- the maximal overlap discrete wavelet transform (MODWT), the discrete wavelet transform (DWT) and the continuous wavelet transform (CWT). These transforms are among others applied to the analysis of the time-varying character of variability in the time series, to the detection of events of significant changes of variability, to the removal of noise in the time series (denoising) and to the time-scale analysis of the relationship of two time series. The analyzed time series used in this thesis are the logarithm of the Garman-Klass estimate of the historical volatility, the time series of stock returns and the logarithm of the monthly inflation rate. In some cases artificial time series are analyzed. The procedures and methods introduced in the thesis might be well implemented in the analysis of other economic and financial time series. The contribution of the thesis is a brief and easy-to-use compilation of the wavelet theory and the application of the wavelet transform to such financial and economic time series, where such an analysis tool has never been applied before. New insights into the properties of time series are thus obtained, insights, which might be hardly recovered by traditional means and methods.

Resumo: Neste trabalho é feito um estudo sobre os métodos de redução de ruído aditivo em sinais de voz baseados em wavelets e, através deste estudo, propõe-se um novo método de redução de ruído em sinais de voz no domínio wavelet. O princípio básico da maioria dos métodos de redução de ruído baseados em wavelets é a determinação e aplicação de um limiar, que permite bons resultados para sinais contaminados por ruído branco, mas não são eficientes no processamento de sinais contaminados por ruído colorido, que é o tipo de ruído mais comum em situações reais. Nesses métodos, o limiar, geralmente, é calculado nos intervalos de silêncio e aplicado em todo o sinal. Os coeficientes no domínio wavelet são comparados com este limiar e aqueles que estão abaixo deste valor são eliminados, fazendo assim uma aplicação linear deste limiar. Esta eliminação acaba causando descontinuidades no tempo e na freqüência no sinal processado. Além disso, a forma com que o limiar é calculado pode degradar os trechos de voz do sinal processado, principalmente nos casos em que o limiar depende fortemente da última janela do último trecho de silêncio. O método proposto neste trabalho também é baseado em corte por limiar, mas em vez de uma aplicação linear do limiar, ele faz uma aplicação não-linear, o que evita as descontinuidades causadas por outros algoritmos. O limiar é calculado nos trechos de silêncio e não depende apenas da última janela do último trecho de silêncio, mas sim de todas as janelas, já que este limiar é uma média de todos os limiares calculados neste trecho. Isto faz com que a redução do ruído seja mais uniforme e introduza menos distorções no sinal processado. Além disso, nos trechos de voz ainda é calculado um novo limiar que também será usado, em conjunto com o limiar calculado no silêncio. Isto faz com que a energia da janela que... (Resumo completo, clicar acesso eletrônico abaixo). / Abstract: In this work a study of additive noise reduction in speech based on wavelets is presented and, based on this study a new noise reduction method in speech in the wavelet domain is proposed. The basic idea of most methods of noise reduction based on wavelets is the determination and application of a threshold, that produces good results for signals contaminated by white noise, but they are not very efficient in processing signals contaminated by colored noise, which is more common in real situations. In those methods, the threshold, generally, is calculated in the silence intervals and applied to the whole signal. The coefficients in the wavelet domain are compared with this threshold and those that are below this value are eliminated, making a linear application of this threshold. This elimination causes discontinuities in time and frequency of the processed signal. Besides, the way that the threshold is computed can degrade the voice segments of the processed signal, principally when the threshold depends strongly on the last window of the last silence segment. The proposed method in this work is also based in thresholding, but, instead of a linear application of the threshold, it makes a non-linear application, which avoids the discontinuities caused by other algorithms. The threshold is calculated in the silence segments and is not dependent only on the last window of the last silence segment, but of all the windows, since this threshold is an average of all thresholds calculated in this segment. It makes noise reduction more uniform and introduces less distortion in the processed signal. Besides, in the voice segments a new threshold is calculated that will be also used with the threshold calculated in the silence. It makes that the energy of the window that is being processed is also considered. This way, it is... (Complete abstract, click electronic address below). / Orientador: Francisco Villarreal Alvarado / Coorientador: Jozué Vieira Filho / Banca: Carlos Roberto Minussi / Banca: Fernando Oscar Runstein / Banca: Roberto Kawakami Harrop Galvão / Banca: Ricardo Tokio Higuti / Doutor