No description available.

No description available.

No description available.

No description available.

Saturn's ring system is actually comprised of a multitude of separate rings, yet each of these rings has areas with more or less constant structural properties which are hard to uncover by observation alone. By measuring stellar occultations, data is collected in the form of Poisson counts (of over 6 million observations) which need to be denoised in order to find these areas with constant properties. At present, these areas are found by visual inspection or examining moving averages, which is hard to do when the amount of data is huge. It is also impossible to do this using the changepoint analysis-based method by Scargle (1998, 2005). For the purpose of finding areas of constant Poisson intensity, a state-of-the-art Haar-Fisz algorithm for Poisson intensity estimation is employed. This algorithm is based on wavelet-like transformation of the original data and subsequent denoising, a methodology originally developed by Nason and Fryzlewicz (2005). We apply the HaarFisz transform to the original data, which normalizes the noise level, then apply the Haar wavelet transform and threshold wavelet coefficients. Finally, we apply the inverse Haar-Fisz transform to recover the Poisson intensity function. We implement the algorithm using R programming language. The program was first tested using synthetic data and then applied to original Saturn ring observations, resulting in a quick, easy method to resolve data into discrete blocks with equal mean average intensities.

Eight roughness configurations in Clemson boundary layer wind tunnel are presented. For these configurations, flow parameters such as turbulent intensities, integral length scales, large- and small- scale turbulence, and spectra of velocity components of the wind are obtained and studied to the simulated turbulence. At the same time, new analyzing tools, orthogonal wavelet techniques, are applied to provide additional information in time domain. This makes it possible to study the intermittency event, one important characteristic associated with pressure peak activities in turbulence. Three parameters, scale energy, intermittency factor and intermittency energy are defined. Variation of these quantities as a result of different configuration is discussed. Finally, the corresponding variations in measured pressure peaks in relation with the variations of configuration as well as with the intermittency parameters are investigated. The work here is of important significance for future wind tunnel and field data comparison, and this could help to find the best simulation among all configurations. / Master of Science

Methods for digital image compression have been the subject of much study over the past decade. Advances in wavelet transforms and quantization methods have produced algorithms capable of surpassing the existing image compression standards like the Joint Photographic Experts Group (JPEG) algorithm. For best performance in image compression, wavelet transforms require filters that combine a number of desirable properties, such as orthogonality and symmetry. However, the design possibilities for wavelets are limited because they cannot simultaneously possess all of these desirable properties. The relatively new field of multiwavelets shows promise in removing some of the limitations of wavelets. Multiwavelets offer more design options and hence can combine all desirable transform features. The few previously published results of multiwavelet-based image compression have mostly fallen short of the performance enjoyed by the current wavelet algorithms. This thesis presents new multiwavelet transform methods and measurements that verify the potential benefits of multiwavelets. Using a zerotree quantization scheme modified to better match the unique decomposition properties of multiwavelets, it is shown that the latest multiwavelet filters can give performance equal to, or in many cases superior to, the current wavelet filters. The performance of multiwavelet packets is also explored for the first time and is shown to be competitive to that of wavelet packets in some cases. The wavelet and multiwavelet filter banks are tested on a much wider range of images than in the usual literature, providing a better analysis of the benefits and drawbacks of each. NOTE: (03/2007) An updated copy of this ETD was added after there were patron reports of problems with the file. / Master of Science

The success of any transform coding technique depends on how well the basis functions represent the signal features. The discrete wavelet transform (DWT) performs a multiresolution analysis of a signal; this enables an efficient representation of smooth and detailed signal regions. Furthermore, computationally efficient algorithms exist for computing the DWT. For these reasons, recent image compression standards such as JPEG2000 use the wavelet transform. It is well known that orthogonality and symmetry are desirable transform properties in image compression applications. It is also known that the scalar wavelet transform does not possess both properties simultaneously. Multiwavelets overcome this limitation; the multiwavelet transform allows orthogonality and symmetry to co-exist. However recently reported image compression results indicate that the scalar wavelets still outperform the multiwavelets in terms of peak signal-to-noise ratio (PSNR). In a multiwavelet transform, the balancing order of the multiwavelet is indicative of its energy compaction efficiency (usually a higher balancing order implies lower mean-squared-error, MSE, in the compressed image). But a high balancing order alone does not ensure good image compression performance. Filter bank characteristics such as shift-variance, magnitude response, symmetry and phase response are important factors that also influence the MSE and perceived image quality. This thesis analyzes the impact of these multiwavelet characteristics on image compression performance. Our analysis allows us to explain---for the first time---reasons for the small performance gap between the scalar wavelets and multiwavelets. We study the characteristics of five balanced multiwavelets (and 2 unbalanced multiwavelets) and compare their image compression performance for grayscale images with the popular (9,7)-tap and (22,14)-tap biorthogonal scalar wavelets. We use the well-known SPIHT quantizer in our compression scheme and utilize PSNR and subjective quality measures to assess performance. We also study the effect of incorporating a human visual system (HVS)-based transform model in our multiwavelet compression scheme. Our results indicate those multiwavelet properties that are most important to image compression. Moreover, the PSNR and subjective quality results depict similar performance for the best scalar wavelets and multiwavelets. Our analysis also shows that the HVS-based multiwavelet transform coder considerably improves perceived image quality at low bit rates. / Master of Science

No / We have studied the performance of multidimensional signaling techniques using wavelets based modulation within an orthogonally multiplexed communication system. The discrete wavelets transform and wavelet packet modulation techniques have been studied using Daubechies 2 and 8, Biothogonal1.5 and 3.1 and reverse Biorthognal 1.5 and 3.1 wavelets in the presence of Rayleigh multipath fading channels with AWGN. Results showed that DWT based systems outperform WPM systems both in terms of BER vs. SNR performance as well as processing. The performances of two different equalizations techniques, namely zero forcing (ZF) and minimum mean square error (MMSE), were also compared using DWT. When the channel is modeled using Rayleigh multipath fading, AWGN and ISI both techniques yield similar performance.

Koopman theory is widely used for data-driven modeling of nonlinear dynamical systems. One of the well-known algorithms that stem from this approach is the Extended Dynamic Mode Decomposition (EDMD), a data-driven algorithm for uncontrolled systems. In this thesis, we will start by discussing the EDMD algorithm. We will discuss how this algorithm encompasses Dynamic Mode Decomposition (DMD), a widely used data-driven algorithm. Then we will extend our discussion to input-output systems and identify ways to extend the Koopman Operator Theory to input-output systems. We will also discuss how various algorithms can be identified as instances of this framework. Special care is given to Wavelet-based Dynamic Mode Decomposition (WDMD). WDMD is a variant of DMD that uses only the input and output data. WDMD does that by generating auxiliary states acquired from the Wavelet transform. We will show how the action of the Koopman operator can be simplified by using the Wavelet transform and how the WDMD algorithm can be motivated by this representation. We will also introduce a slight modification to WDMD that makes it more robust to noise. / Master of Science / To analyze a real-world phenomenon we first build a mathematical model to capture its behavior. Traditionally, to build a mathematical model, we isolate its principles and encode it into a function. However, when the phenomenon is not well-known, isolating these principles is not possible. Hence, rather than understanding its principles, we sample data from that phenomenon and build our mathematical model directly from this data by using approximation techniques. In this thesis, we will start by focusing on cases where we can fully observe the phenomena, when no external stimuli are present. We will discuss how some algorithms originating from these approximation techniques can be identified as instances of the Extended Dynamic Mode Decomposition (EDMD) algorithm. For that, we will review an alternative approach to mathematical modeling, called the Koopman approach, and explain how the Extended DMD algorithm stems from this approach. Then we will focus on the case where there is external stimuli and we can only partially observe the phenomena. We will discuss generalizations of the Koopman approach for this case, and how various algorithms that model such systems can be identified as instances of the EDMD algorithm adapted for this case. Special attention is given to the Wavelet-based Dynamic Mode Decomposition (WDMD) algorithm. WDMD builds a mathematical model from the data by borrowing ideas from Wavelet theory, which is used in signal processing. In this way, WDMD does not require the sampling of the fully observed system. This gives WDMD the flexibility to be used for cases where we can only partially observe the phenomena. While showing that WDMD is an instance of EDMD, we will also show how Wavelet theory can simplify the Koopman approach and thus how it can pave the way for an easier analysis.