The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. / The main objective of this study is to find a wavelet-based, feature extracting algorithm for push-to-talk transmitter identification. A distance-measure algorithm is introduced to classify signals belonging to one of four transmitters. The signals are first preprocessed to put them into a form suitable for wavelet analysis. The preprocessing scheme includes taking the envelopes and differentials. Median filtering is also applied to the outputs of the wavelet transform. The distance algorithm uses local extrema of the wavelet coefficients, and computes the distance between the local extrema of a template and the processed signals. A small distance implies high similarity . A signal from each transmitter is selected as a template. A small distance measure indicates that the signal belongs to the transmitter from which the template originated. The distance algorithm can classify correctly the four different signal sets provided for the research. Even at lower signal-to-noise levels, good identification is achieved.

Modern technologies have eased the way for adversaries to bypass the conventional identity authentication and identification processes; hence security systems have been developed to a great extent for protection of privacy and security of identities in different applications. The focus of this thesis is digital watermarking, security and privacy, as well as the ability to employ electrocardiogram as a method to enhance the security and privacy level. A high capacity reversible multiple watermarking scheme is introduced to mainly target the medical images. Furthermore, the use of ECG biometric signals in the form of the embedded watermark is studied. Experimental results indicate that the reversible data hiding scheme outperforms other approaches in the literature in terms of payload capacity and marked image quality. Results from the ECG mark embedding also show that no major degradation in performance is noticeable compared to the case where no watermarking is needed.

Modern technologies have eased the way for adversaries to bypass the conventional identity authentication and identification processes; hence security systems have been developed to a great extent for protection of privacy and security of identities in different applications. The focus of this thesis is digital watermarking, security and privacy, as well as the ability to employ electrocardiogram as a method to enhance the security and privacy level. A high capacity reversible multiple watermarking scheme is introduced to mainly target the medical images. Furthermore, the use of ECG biometric signals in the form of the embedded watermark is studied. Experimental results indicate that the reversible data hiding scheme outperforms other approaches in the literature in terms of payload capacity and marked image quality. Results from the ECG mark embedding also show that no major degradation in performance is noticeable compared to the case where no watermarking is needed.

The construction of the generalized continuous wavelet transform (GCWT) on Hilbert spaces is a special case of the coherent state transform construction, where the coherent state system arises as an orbit of an admissible vector under a strongly continuous unitary representation of a locally compact group. In this thesis we extend this construction to the setting of Hilbert C*-modules. In particular, we define a coherent state transform and a GCWT on Hilbert modules. This construction gives a reconstruction formula and a resolution of the identity formula analogous to those found in the Hilbert space setting. Moreover, the existing theory of standard normalized tight frames in finite countably generated Hilbert modules can be viewed as a discrete case of this construction We also show that the image space of the coherent state transform on Hilbert module is a reproducing kernel Hilbert module. We discuss the kernel and the intertwining property of the group coherent state transform.

The subject of my thesis is a design of the methods optimizing, the acquisition of MR signals when small objects measure. The thesis is divided into several parts in order to give a deeper knowledge of the problem. The first part focuses on the theory associated with NMR (Nuclear Magnetic Resonance) and SNR (signal-to-noise ratio). The practical verification of the theory follows. The conclusion of this work is focused on MR images filtering by use of wavelet transform to suppress a noise in the image. The method optimization of MR acquisition parameters for the measurement of small objects is then distributed to the entire work.

There are two critical research needs for the study of hydrocarbon combustion in high speed flows: 1) combustion diagnostics with adequate temporal and spatial resolution, and 2) mathematical techniques that can extract key information from large datasets. The goal of this work is to address these needs, respectively, by the use of high speed and multi-perspective chemiluminescence and advanced mathematical algorithms. To obtain the measurements, this work explored the application of high speed chemiluminescence diagnostics and the use of fiber-based endoscopes (FBEs) for non-intrusive and multi-perspective chemiluminescence imaging up to 20 kHz. Non-intrusive and full-field imaging measurements provide a wealth of information for model validation and design optimization of propulsion systems. However, it is challenging to obtain such measurements due to various implementation difficulties such as optical access, thermal management, and equipment cost. This work therefore explores the application of FBEs for non-intrusive imaging to supersonic propulsion systems. The FBEs used in this work are demonstrated to overcome many of the aforementioned difficulties and provided datasets from multiple angular positions up to 20 kHz in a supersonic combustor. The combustor operated on ethylene fuel at Mach 2 with an inlet stagnation temperature and pressure of approximately 640 degrees Fahrenheit and 70 psia, respectively. The imaging measurements were obtained from eight perspectives simultaneously, providing full-field datasets under such flow conditions for the first time, allowing the possibility of inferring multi-dimensional measurements. Due to the high speed and multi-perspective nature, such new diagnostic capability generates a large volume of data and calls for analysis algorithms that can process the data and extract key physics effectively. To extract the key combustion dynamics from the measurements, three mathematical methods were investigated in this work: Fourier analysis, proper orthogonal decomposition (POD), and wavelet analysis (WA). These algorithms were first demonstrated and tested on imaging measurements obtained from one perspective in a sub-sonic combustor (up to Mach 0.2). The results show that these algorithms are effective in extracting the key physics from large datasets, including the characteristic frequencies of flow—flame interactions especially during transient processes such as lean blow off and ignition. After these relatively simple tests and demonstrations, these algorithms were applied to process the measurements obtained from multi-perspective in the supersonic combustor. compared to past analyses (which have been limited to data obtained from one perspective only), the availability of data at multiple perspective provide further insights into the flame and flow structures in high speed flows. In summary, this work shows that high speed chemiluminescence is a simple yet powerful combustion diagnostic. Especially when combined with FBEs and the analyses algorithms described in this work, such diagnostics provide full-field imaging at high repetition rate in challenging flows. Based on such measurements, a wealth of information can be obtained from proper analysis algorithms, including characteristic frequency, dominating flame modes, and even multi-dimensional flame and flow structures. / Ph. D.

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Heart rate variability (HRV) analysis has proved to be an important tool for assessing autonomic nervous system. For instance, it has been used during dipyridamole echocardiographic test to differentiate ischemic from nonischemic responses [6]. RR Interval analysis can provide additional information that can lead to early detection of a possible change in the activity of the autonomic nervous system. HRV analysis can be done using Wavelet Transform. This thesis presents a modification of an existing algorithm for extracting the R-R interval from EKG data sets and the use of wavelet transform (WT) technique to compute the timerequency domain energy quantities. The project used data obtained previously from a study of the effects of two pharmacological agents, atropine and propranolol, on laboratory rats. Results showed that the ratio of high frequency energy over the total energy (HF/total) of atropine treated rats was higher than baseline (control).

Yes / A new wavelet transform (WT) is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a fractional domain. It exploits the combined advantages of WT and fractional Fourier transform (FrFT). The transform permits the identification of a transformed function based on the fractional rotation in time-frequency plane. The fractional rotation is then used to identify individual fractional daughter wavelets. This study is, for convenience, limited to one-dimension. Approach for discussing two or more dimensions is shown.