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.

Digital image watermarking is used to protect the copyright of digital images. In this thesis, a novel blind logo image watermarking technique for RGB images is proposed. The proposed technique exploits the error correction capabilities of the Human Visual System (HVS). It embeds two different watermarks in the wavelet/multiwavelet domains. The two watermarks are embedded in different sub-bands, are orthogonal, and serve different purposes. One is a high capacity multi-bit watermark used to embed the logo, and the other is a 1-bit watermark which is used for the detection and reversal of geometrical attacks. The two watermarks are both embedded using a spread spectrum approach, based on a pseudo-random noise (PN) sequence and a unique secret key. Robustness against geometric attacks such as Rotation, Scaling, and Translation (RST) is achieved by embedding the 1-bit watermark in the Wavelet Transform Modulus Maxima (WTMM) coefficients of the wavelet transform. Unlike normal wavelet coefficients, WTMM coefficients are shift invariant, and this important property is used to facilitate the detection and reversal of RST attacks. The experimental results show that the proposed watermarking technique has better distortion parameter detection capabilities, and compares favourably against existing techniques in terms of robustness against geometrical attacks such as rotation, scaling, and translation.

This thesis deals with analysis of dynamic forces and vibrations created during cutting with saw. The analysis is done on both simulation and experimental level. Acquired signals are evaluated with signal tools as STFT, CWT and DWT.

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.

Rotating machinery is a critical asset of industrial plants worldwide. Bearings and gearboxes are two of the most common components found in rotating machinery of industrial plants. The malfunction of bearings and gearboxes lead the machine to fail and often these failures occur catastrophically leading to personnel injuries. Therefore it is of high importance to identify the deterioration at an early stage. Among the techniques applied to detect damage in rotating machinery, acoustic emission has been a prevalent field of research for its potential to detect defects at an earlier stage than other more established techniques such as vibration analysis and oil analysis. However, to reliably detect the fault at an early stage de-noising techniques often must be applied to reduce the AE noise generated by neighbouring components and normal component operation. For this purpose a novel signal processing algorithm has been developed combining Wavelet Packets as a pre-processor, Hilbert Transform, Autocorrelation function and Fast Fourier transform. The combination of these techniques allows identification of g repetitive patterns in the AE signal that are attributable to bearing and gear damage. The enhancement for early stage defect detection in bearings and gears provided by this method is beneficial in planning maintenance in advance, reducing machinery down-time and consequently reducing the costs associated with bearing breakdown. The effectiveness of the proposed method has been investigated experimentally using seeded and naturally developed defects in gears and bearings. In addition, research into the optimal Wavelet Packet node that offers the best de-noising results has been performed showing that the 250-750 kHz band gives the best SNR results. The detection of shaft angular misalignment using Acoustic Emission has been investigated and compared with acceleration spectra. The results obtained show enhancements of AE in detection shaft angular misalignment over vibration analysis in SNR and stability with varying operational conditions.