A scaling model based on an effective Gol'dberg number is proposed for predicting the presence of cumulative nonlinear distortions in the acoustic waveforms produced by high-speed jets. Two acoustic length scales, the shock formation distance and the absorption length are expressed in terms of jet exit parameters. This approach allows one to compute the degree of cumulative nonlinear distortion in a full-scale scenario, from laboratory-scale observations, or vice versa. Surveys of the acoustic pressure waveforms emitted by a laboratory-scale, shock-free and unheated Mach 3 jet are used to support the findings of the model. These acoustic waveforms are acquired on a planar grid in an acoustically treated and range-restricted environment. Various statistical metrics are employed to examine the degree of local and cumulative nonlinearity in the measured waveforms and their temporal derivatives. This includes skewness, kurtosis, the number of zero crossings in the waveform, a wave steepening factor, the Morfey-Howell nonlinearity indicator and an application of the generalized Burgers equation. It is advocated that in order for the Morfey-Howell indicator to be used as an investigative tool for the presence of cumulative nonlinear waveform distortion, that it be applied as a multi-point indicator. Based on findings of the model and the spatial topography of the metrics, it is concluded that cumulative nonlinear steepening effects are absent in the current data set. This implies that acoustic shock-structures in the waveforms are generated by local mechanisms in, or in close vicinity to, the jet's hydrodynamic region. Furthermore, these shock-structures induce the crackle noise component. The research aims to quantify crackle in a temporal and spectral fashion, and is motivated by the fact that (1) it is perceived as the most annoying component of jet noise, (2) no unique measures of crackle exist, and (3) significant reductions in jet noise will be achieved when crackle can be controlled. A unique detection algorithm is introduced which isolates the shock-structures in the temporal waveform that are responsible for crackle. Ensemble-averages of the identified waveform sections are employed to gain an in-depth understanding of the crackling structures. Moreover, PDF's of the temporal intermittence of these shocks reveal modal trends and show evidence that crackling shock-structures are present in groups of multiple shocks. A spectral measure of crackle is considered by using wavelet-based time-frequency analyses. The increase in sound energy is computed by considering the global pressure spectra of the waveforms and the ones that represent the spectral behavior during instances of crackle. This energy-based metric is postulated to be an appropriate metric for the level of crackle. / text

Monitoring of engineered systems consists of characterizing the normal behavior of the system and tracking departures from it. Techniques to monitor a system can be split into two classes based on their use of inputs and outputs of the system. Systems-based monitoring refers to the case when both inputs and outputs of a system are available and utilized. Conversely, symptomatic monitoring refers to the case when only outputs of the system are available. This thesis extended symptomatic and systems-based monitoring of biomedical systems via the use of non-stationary signal processing and advanced monitoring methods. Monitoring of various systems of the human body is encumbered by several key hurdles. First, current biomedical knowledge may not fully comprehend the extent of inputs and outputs of a particular system. In addition, regardless of current knowledge, inputs may not be accessible and outputs may be, at best, indirect measurements of the underlying biological process. Finally, even if inputs and outputs are measurable, their relationship may be highly nonlinear and convoluted. These hurdles require the use of advanced signal processing and monitoring approaches. Regardless of the pursuit of symptomatic or system-based monitoring, the aforementioned hurdles can be partially overcome by using non-stationary signal analysis to reveal the way frequency content of biomedical signals change over time. Furthermore, the use of advanced classification and monitoring methods facilitated reliable differentiation between various conditions of the monitored system based on the information from non-stationary signal analysis. The human brain was targeted for advancement of symptomatic monitoring, as it is a system responding to a plethora internal and external stimuli. The complexity of the brain makes it unfeasible to realize system-based monitoring to utilize all the relevant inputs and outputs for the brain. Further, measurement of brain activity (outputs), in the indirect form of electroencephalogram (EEG), remains a workhorse of brain disorder diagnosis. In this thesis, advanced signal processing and pattern recognition methods are employed to devise and study an epilepsy detection and localization algorithm that outperforms those reported in literature. This thesis also extended systems-based monitoring of human biomedical systems via advanced input-output modeling and sophisticated monitoring techniques based on the information from non-stationary signal analysis. Explorations of system-based monitoring in the NMS system were driven by the fact that joint velocities and torques can be seen NMS responses to electrical inputs provided by the central nervous system (CNS) and the electromyograph (EMG) provides an indirect measurement of CNS excitations delivered to the muscles. Thus, both inputs and outputs of this system are more or less available and one can approach its monitoring via the use of system-based approaches. / text

This dissertation has been motivated by the increasing application of sensing technologies in structural health monitoring. Many wireless sensor techniques exist for structural health monitoring while a challenge faced is the finite lifetime of batteries. The objective of this dissertation is to develop passive wireless technology to provide early warning of conditions that damage the structure. In this dissertation, sensing mechanism is proposed based on time and frequency domain characteristics of magneto-inductive (MI) waves. Experimental results are also presented to demonstrate the sensing mechanism. MI waves are predominantly magnetic waves that are supported in periodic arrays of magnetically coupled resonators and propagate within a narrow frequency band around the resonant frequency. The array is to be embedded in a structure and different types of transducers can be integrated for different sensing applications. With the onset of structure defect, the transducer introduces an impedance discontinuity that generates reflected MI waves along the array, which are monitored and processed by Smoothed Wigner-Ville distribution (WVD) to extract time-of-flight for frequency components in the narrow passband. The transmission and reflection coefficients of MI waves are also investigated based on the lumped-element circuit model of the array. Based on MI waves travel time, amplitude and group velocity, the position and severity of structure defect are decided. The sensing mechanisms for different distribution of defects are proposed. The validity of the sensing mechanism is examined in experiments. The guided wave testing is implemented in one-dimensional square-shaped printed spiral resonators with Q-factor of 161 at 13.6 MHz. It demonstrates that low MI waves propagation loss is achieved with value of 0.098 dB per element at mid-band with center-to-center distance of half an inch. A pitch-catch measurement system is built to capture traveling MI signal in resonant element and extract group velocity, and a pulse-echo measurement system is designed to monitor reflected MI signal and locate structure discontinuity. In both measurement systems, MI waves are excited with wide bandwidth voltage pulse, and a digitizer is attached to sense the MI signal in a specific resonant element circuit. A baseline signal is obtained from the healthy state to use as reference and comparison with the test case using pitch-catch system. The test signal subtracted from baseline signal infers the structure damage information with time and frequency domain characteristics. It can offer an effective method to estimate the structure discontinuity location, severity and type of damage. The experimental results are consistent with the theoretical predictions. At the end, future directions for the research to integrate with other technologies are suggested. / text

The visual system receives a series of fluctuating light patterns on the retina, yet visual perception is strikingly different from this unorganized and ambiguous input. Thus visual processes must organize the input into coherent units, or objects, and segregate them from others. These processes, collectively called perceptual organization, are fundamental to our ability to perceive and interact with objects in the world. Nevertheless, they are not yet understood, perhaps because serial, hierarchical assumptions that were long held impeded progress. In a series of experiments, this dissertation investigated the mechanisms that contribute to perceptual organization and ultimately to our ability to perceive objects. A new hypothesis is that during the course of object assignment potential objects on either side of a border are accessed on a fast pass of processing and engage in inhibitory competition for object status; the winner is perceived as the object and the loser is suppressed, leading that region to be seen as part of the shapeless background. Previous research suggested that at least shape level representations are accessed on the fast pass of processing before object assignment. In the first series of experiments (Chapter 1), we found that meaning (semantics) is also accessed on the fast pass of processing for regions that are ultimately perceived as shapeless grounds. This finding contradicts traditional feed-forward theories of perception that assumed that meaning is accessed only for figures after object assignment. The experiments in Chapter 2 examine activity in the alpha band of the EEG, which has been used as an index of inhibition. More alpha activity was observed when participants viewed stimuli designed such that there was more competition for figural status from the region ultimately perceived as the ground. The results support the proposal that inhibitory competition occurs during the course of object perception, and these results are the first online measure of competition during figure assignment. The final series of experiments (Chapter 3) investigated how quickly saccadic behaviors that required perceptual organization can be initiated. The experiments show that participants can initiate saccades that are based on perceptual organization approximately 200 ms after stimulus onset, much faster than was assumed on feed-forward models of perception. Collectively, these experiment support models of object perception that involve the mutual interaction and competition of objects properties via feedforward and iterative feedback processing, and the eventual suppression of the losing ground regions before object assignment.

Time-frequency analysis is a powerful tool for signal analysis and processing. The Fourier transform and wavelet transforms are used extensively as is the Short-Time Fourier Transform (or Gabor transform). In 1996 the Stockwell transform was introduced to maintain the phase of the Fourier transform, while also providing the progressive resolution of the wavelet transform. The discrete orthonormal Stockwell transform is a more efficient, less redundant transform with the same properties. There has been little work on mathematical properties of the Stockwell transform, particularly how it behaves under operations such as translation and modulation. Previous results do discuss a resolution of the identity, as well as some of the function spaces that may be associated with it [2]. We extend the resolution of the identity results, and behaviour under translation, modulation, convolution and differentiation. boundedness and continuity properties are also developed, but the function spaces associated with the transform are unrelated to the focus of this thesis. There has been some work on image processing using the Stockwell transform and discrete orthonormal Stockwell transform. The tests were quite preliminary. In this thesis, we explore some of the mathematics of the Stockwell transform, examining properties, and applying it to various continuous examples. The discrete orthonormal Stockwell transform is compared directly with Newland’s harmonic wavelet transform, and we extend the definition to include varitions, as well as develop the discrete cosine based Stockwell transform. All of these discrete transforms are tested against current methods for image compression.

This thesis presents results on the description of plasma waves in terms of wavepackets. The wave field is decomposed into a distribution of wavepackets in a space of position, wavevector, time, and frequency. A complex structure joining each pair of Fourier conjugate variables into a single complex coordinate allows the efficient derivation of equations of motion for the phase space distribution by exploiting its analytic properties. The Wick symbol calculus, a mathematical tool generalizing many convenient properties of the Fourier transform to a local setting, is used to derive new exact phase space equations which maintain full information on the phase of the waves and include effects nonlocal in phase space such as harmonic generation. A general purpose asymptotic expansion of the Wick symbol product formula is used to treat dispersion, refraction, photon acceleration, and ponderomotive forces. Examples studied include the nonlinear Schrödinger equation, mode conversion, and the Vlasov equation. The structure of partially coherent wave fields is understood in terms of zeros in the phase space distribution caused by dislocations in its complex phase which are shown to be correlated with the field entropy. Simulations of plasma heating by crossing electron beams are understood by representing the resulting plasma waves in phase space. The local coherence properties of the beam driven Langmuir waves are studied numerically.

abstract: Peptide microarrays have been used in molecular biology to profile immune responses and develop diagnostic tools. When the microarrays are printed with random peptide sequences, they can be used to identify antigen antibody binding patterns or immunosignatures. In this thesis, an advanced signal processing method is proposed to estimate epitope antigen subsequences as well as identify mimotope antigen subsequences that mimic the structure of epitopes from random-sequence peptide microarrays. The method first maps peptide sequences to linear expansions of highly-localized one-dimensional (1-D) time-varying signals and uses a time-frequency processing technique to detect recurring patterns in subsequences. This technique is matched to the aforementioned mapping scheme, and it allows for an inherent analysis on how substitutions in the subsequences can affect antibody binding strength. The performance of the proposed method is demonstrated by estimating epitopes and identifying potential mimotopes for eight monoclonal antibody samples. The proposed mapping is generalized to express information on a protein's sequence location, structure and function onto a highly localized three-dimensional (3-D) Gaussian waveform. In particular, as analysis of protein homology has shown that incorporating different kinds of information into an alignment process can yield more robust alignment results, a pairwise protein structure alignment method is proposed based on a joint similarity measure of multiple mapped protein attributes. The 3-D mapping allocates protein properties into distinct regions in the time-frequency plane in order to simplify the alignment process by including all relevant information into a single, highly customizable waveform. Simulations demonstrate the improved performance of the joint alignment approach to infer relationships between proteins, and they provide information on mutations that cause changes to both the sequence and structure of a protein. In addition to the biology-based signal processing methods, a statistical method is considered that uses a physics-based model to improve processing performance. In particular, an externally developed physics-based model for sea clutter is examined when detecting a low radar cross-section target in heavy sea clutter. This novel model includes a process that generates random dynamic sea clutter based on the governing physics of water gravity and capillary waves and a finite-difference time-domain electromagnetics simulation process based on Maxwell's equations propagating the radar signal. A subspace clutter suppression detector is applied to remove dominant clutter eigenmodes, and its improved performance over matched filtering is demonstrated using simulations. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2014

abstract: A signal with time-varying frequency content can often be expressed more clearly using a time-frequency representation (TFR), which maps the signal into a two-dimensional function of time and frequency, similar to musical notation. The thesis reviews one of the most commonly used TFRs, the Wigner distribution (WD), and discusses its application in Fourier optics: it is shown that the WD is analogous to the spectral dispersion that results from a diffraction grating, and time and frequency are similarly analogous to a one dimensional spatial coordinate and wavenumber. The grating is compared with a simple polychromator, which is a bank of optical filters. Another well-known TFR is the short time Fourier transform (STFT). Its discrete version can be shown to be equivalent to a filter bank, an array of bandpass filters that enable localized processing of the analysis signals in different sub-bands. This work proposes a signal-adaptive method of generating TFRs. In order to minimize distortion in analyzing a signal, the method modifies the filter bank to consist of non-overlapping rectangular bandpass filters generated using the Butterworth filter design process. The information contained in the resulting TFR can be used to reconstruct the signal, and perfect reconstruction techniques involving quadrature mirror filter banks are compared with a simple Fourier synthesis sum. The optimal filter parameters of the rectangular filters are selected adaptively by minimizing the mean-squared error (MSE) from a pseudo-reconstructed version of the analysis signal. The reconstruction MSE is proposed as an error metric for characterizing TFRs; a practical measure of the error requires normalization and cross correlation with the analysis signal. Simulations were performed to demonstrate the the effectiveness of the new adaptive TFR and its relation to swept-tuned spectrum analyzers. / Dissertation/Thesis / M.S. Electrical Engineering 2012

abstract: The use of electromyography (EMG) signals to characterize muscle fatigue has been widely accepted. Initial work on characterizing muscle fatigue during isometric contractions demonstrated that its frequency decreases while its amplitude increases with the onset of fatigue. More recent work concentrated on developing techniques to characterize dynamic contractions for use in clinical and training applications. Studies demonstrated that as fatigue progresses, the EMG signal undergoes a shift in frequency, and different physiological mechanisms on the possible cause of the shift were considered. Time-frequency processing, using the Wigner distribution or spectrogram, is one of the techniques used to estimate the instantaneous mean frequency and instantaneous median frequency of the EMG signal using a variety of techniques. However, these time-frequency methods suffer either from cross-term interference when processing signals with multiple components or time-frequency resolution due to the use of windowing. This study proposes the use of the matching pursuit decomposition (MPD) with a Gaussian dictionary to process EMG signals produced during both isometric and dynamic contractions. In particular, the MPD obtains unique time-frequency features that represent the EMG signal time-frequency dependence without suffering from cross-terms or loss in time-frequency resolution. As the MPD does not depend on an analysis window like the spectrogram, it is more robust in applying the timefrequency features to identify the spectral time-variation of the EGM signal. / Dissertation/Thesis / M.S. Electrical Engineering 2012

Cette thèse s'inscrit dans le contexte de l'analyse/transformation/synthèse des signaux audio utilisant des représentations temps-fréquence, de type transformation de Gabor. Dans ce contexte, la complexité des transformations permettant de relier des sons peut être modélisée au moyen de multiplicateurs de Gabor, opérateurs de signaux linéaires caractérisés par une fonction de transfert temps-fréquence, à valeurs complexes, que l'on appelle masque de Gabor. Les multiplicateurs de Gabor permettent deformaliser le concept de filtrage dans le plan temps-fréquence. En agissant de façon multiplicative dans le plan temps-fréquence, ils sont a priori bien adaptés pour réaliser des transformations sonores telles que des modifications de timbre des sons. Dans un premier temps, ce travail de thèses intéresse à la modélisation du problème d'estimation d'un masque de Gabor entre deux signaux donnés et la mise en place de méthodes de calculs efficaces permettant de résoudre le problème. Le multiplicateur de Gabor entre deux signaux n'est pas défini de manière unique et les techniques d'estimation proposées de construire des multiplicateurs produisant des signaux sonores de qualité satisfaisante. Dans un second temps, nous montrons que les masques de Gabor contiennent une information pertinente capable d'établir une classification des signaux,et proposons des stratégies permettant de localiser automatiquement les régions temps-fréquence impliquées dans la différentiation de deux classes de signaux. Enfin, nous montrons que les multiplicateurs de Gabor constituent tout un panel de transformations sonores entre deux sons, qui, dans certaines situations, peuvent être guidées par des descripteurs de timbre / Analysis/Transformation/Synthesis is a generalparadigm in signal processing, that aims at manipulating or generating signalsfor practical applications. This thesis deals with time-frequencyrepresentations obtained with Gabor atoms. In this context, the complexity of a soundtransformation can be modeled by a Gabor multiplier. Gabormultipliers are linear diagonal operators acting on signals, andare characterized by a time-frequency transfer function of complex values, called theGabor mask. Gabor multipliers allows to formalize the conceptof filtering in the time-frequency domain. As they act by multiplying in the time-frequencydomain, they are "a priori'' well adapted to producesound transformations like timbre transformations. In a first part, this work proposes to model theproblem of Gabor mask estimation between two given signals,and provides algorithms to solve it. The Gabor multiplier between two signals is not uniquely defined and the proposed estimationstrategies are able to generate Gabor multipliers that produce signalswith a satisfied sound quality. In a second part, we show that a Gabor maskcontain a relevant information, as it can be viewed asa time-frequency representation of the difference oftimbre between two given sounds. By averaging the energy contained in a Gabor mask, we obtain a measure of this difference that allows to discriminate different musical instrumentsounds. We also propose strategies to automaticallylocalize the time-frequency regions responsible for such a timbre dissimilarity between musicalinstrument classes. Finally, we show that the Gabor multipliers can beused to construct a lot of sounds morphing trajectories,and propose an extension