Incorporating information from the short-time phase spectrum into a feature set for automatic speech recognition (ASR) may possibly serve to improve recognition accuracy. Currently, however, it is common practice to discard this information in favour of features that are derived purely from the short-time magnitude spectrum. There are two reasons for this: 1) the results of some well-known human listening experiments have indicated that the short-time phase spectrum conveys a negligible amount of intelligibility at the small window durations of 20-40 ms used for ASR spectral analysis, and 2) using the short-time phase spectrum directly for ASR has proven di?cult from a signal processing viewpoint, due to phase-wrapping and other problems. In this thesis, we explore the possibility of using short-time phase spectrum information for ASR by considering the two points mentioned above. To address the ?rst point, we conduct our own set of human listening experiments. Contrary to previous studies, our results indicate that the short-time phase spectrum can indeed contribute signi?cantly to speech intelligibility over small window durations of 20-40 ms. Also, the results of these listening experiments, in addition to some ASR experiments, indicate that at least part of this intelligibility may be supplementary to that provided by the short-time magnitude spectrum. To address the second point (i.e., the signal processing di?culties), it may be necessary to transform the short-time phase spectrum into a more physically meaningful representation from which useful features could possibly be extracted. Speci?cally, we investigate the frequency-derivative (or group delay function, GDF) and the time-derivative (or instantaneous frequency distribution, IFD) as potential candidates for this intermediate representation. We have performed various experiments which show that the GDF and IFD may be useful for ASR. We conduct several ASR experiments to test a feature set derived from the GDF. We ?nd that, in most cases, these features perform worse than the standard MFCC features. Therefore, we suggest that a short-time phase spectrum feature set may ultimately be derived from a concatenation of information from both the GDF and IFD representations. For best performance, the feature set may also need to be concatenated with short-time magnitude spectrum information. Further to addressing the two aforementioned points, we also discuss a number of other speech applications in which the short-time phase spectrum has proven to be very useful. We believe that an appreciation for how the short-time phase spectrum has been used for other tasks, in addition to the results of our research, will provoke fellow researchers to also investigate its potential for use in ASR.

Systems biology aims to understand cellular behavior in terms of the spatiotemporal interactions among cellular components, such as genes, proteins and metabolites. Comprehensive visualization tools for exploring multivariate data are needed to gain insight into the physiological processes reflected in these molecular profiles. Data fusion methods are required to integratively study high-throughput transcriptomics, metabolomics and proteomics data combined before systems biology can live up to its potential. In this work I explored mathematical and statistical methods and visualization tools to resolve the prominent issues in the nature of systems biology data fusion and to gain insight into these comprehensive data. In order to choose and apply multivariate methods, it is important to know the distribution of the experimental data. Chi square Q-Q plot and violin plot were applied to all M. truncatula data and V. vinifera data, and found most distributions are right-skewed (Chapter 2). The biplot display provides an effective tool for reducing the dimensionality of the systems biological data and displaying the molecules and time points jointly on the same plot. Biplot of M. truncatula data revealed the overall system behavior, including unidentified compounds of interest and the dynamics of the highly responsive molecules (Chapter 3). The phase spectrum computed from the Fast Fourier transform of the time course data has been found to play more important roles than amplitude in the signal reconstruction. Phase spectrum analyses on in silico data created with two artificial biochemical networks, the Claytor model and the AB2 model proved that phase spectrum is indeed an effective tool in system biological data fusion despite the data heterogeneity (Chapter 4). The difference between data integration and data fusion are further discussed. Biplot analysis of scaled data were applied to integrate transcriptome, metabolome and proteome data from the V. vinifera project. Phase spectrum combined with k-means clustering was used in integrative analyses of transcriptome and metabolome of the M. truncatula yeast elicitation data and of transcriptome, metabolome and proteome of V. vinifera salinity stress data. The phase spectrum analysis was compared with the biplot display as effective tools in data fusion (Chapter 5). The results suggest that phase spectrum may perform better than the biplot. This work was funded by the National Science Foundation Plant Genome Program, grant DBI-0109732, and by the Virginia Bioinformatics Institute. / Ph. D.

The Fourier transform (spectrum) of a signal is a complex function and is characterized by the magnitude and phase spectra. Phase retrieval is the reconstruction of the phase spectrum from the measurements of the magnitude spectrum. Such problems are encountered in imaging modalities such as X-ray crystallography, frequency-domain optical coherence tomography (FDOCT), quantitative phase microscopy, digital holography, etc., where only the magnitudes of the wavefront are detected by the sensors. The phase retrieval problem is ill-posed in general, since an in nite number of signals can have the same magnitude spectrum. Typical phase retrieval techniques rely on certain prior knowledge about the signal, such as its support or sparsity, to reconstruct the signal. A classical result in phase retrieval is that minimum-phase signals have log-magnitude and phase spectra that satisfy the Hilbert integral equations, thus facilitating exact phase retrieval. In this thesis, we demonstrate that there exist larger classes of signals beyond minimum-phase signals, for which exact phase retrieval is possible. We generalize Hilbert integral equations to 2-D, and also introduce a variant that we call the composite Hilbert transform in the context of 2-D periodic signals. Our first extension pertains to a particular type of parametric modelling of 2-D signals. While 1-D minimum-phase signals have a parametric representation, in terms of poles and zeros, there exists no such 2-D counterpart. We introduce a new class of parametric 2-D signals that possess the exact phase retrieval property, that is, their magnitude spectrum completely characterizes the signal. Starting from the magnitude spectrum, a sequence of non-linear operations lead us to a sum-of-exponentials signal, from which the parameters are computed employing concepts from high-resolution spectral estimation such as the annihilating filter and algebraically coupled matrix-pencil methods. We demonstrate that, for this new class of signals, our method outperforms existing techniques even in the presence of noise. Our second extension is to continuous-domain signals that lie in a principal shift-invariant space spanned by a known basis. Such signals are characterized by the basis combining coefficients. These signals need not be minimum-phase, but certain conditions on the coefficients lead to exact phase retrieval of the continuous-domain signal. In particular, we introduce the concept of causal, delta dominant (CDD) sequences, and show that such signals are characterized by their magnitude spectra. This condition pertains to the time/spatial-domain description of the signal, in contrast to the minimum-phase condition, which is described in the spectral domain. We show that there exist CDD sequences that are not minimum-phase, and vice versa. However, finite-length CDD sequences are always minimum-phase. Our method reconstructs the signal from the magnitude spectrum up to ma-chine precision. We thus have a class of continuous-domain signals that are neither causal nor minimum phase, and yet allow for exact phase retrieval. The shift-invariant structure is applicable to modelling signals encountered in imaging modalities such as FDOCT. We next present an application of 2-D phase retrieval to continuous-domain CDD signals in the context of quantiative phase microscopy. We develop sufficient conditions on the interfering reference wave for exact phase retrieval from magnitude measurements. In particular, we show that when the reference wave is a plane wave with magnitude greater that the intensity of the object wave, and when the carrier frequency is larger than the band-width of the object wave, we can reconstruct the object wave exactly. We demonstrate high-resolution reconstruction of our method on USAF target images. Our final and perhaps the most unifying contribution is in developing Hilbert integral equations for 2-D first-quadrant signals and in introducing the notion of generalized minimum-phase signals for both 1-D and 2-D signals. For 2-D continuous-domain, first-quadrant signals, we establish partial Hilbert transform relations between the real and imaginary parts of the spectrum. In the context of 2-D discrete-domain signals, we show that the partial Hilbert transform does not suffice and introduce the notion of composite Hilbert transform and establish the integral equations. We then introduce four classes of signals (combinations of 1-D/2-D and continuous/discrete-domain) that we call generalized minimum-phase signals, which satisfy corresponding Hilbert integral equations between log-magnitude and phase spectra, hence facilitating exact phase retrieval. This class of generalized minimum-phase signals subsumes the well known class of minimum-phase signals. We further show that, akin to minimum-phase signals, these signals also have stable inverses, which are also generalized minimum-phase signals.

In der nichtlinearen Datenreihenanalyse hat sich seit etwa 10 Jahren eine Monte-Carlo-Testmethode etabliert, die Theiler-surrogatmethode, mit Hilfe derer entschieden werden kann, ob eine Datenreihe nichtlinearen Ursprungs sei. Diese Methode wird kritisiert, modifiziert und verallgemeinert. Das, was Theiler untersuchen will braucht andere Surrogatmethoden, die hier konstruiert werden. Und das, was Theiler untersucht braucht gar keine Monte-Carlo-Methoden. Mit Hilfe des in der Arbeit eingeführten Begriffs des Phasensignals werden Testmöglichkeiten dargelegt und Beziehungen zwischen den nichtlinearen Eigenschaften der Zeitreihe und deren Phasenspektrum erforscht. Das Phasensignal wird aus dem Phasenspektrum der Zeitreihe hergeleitet und registriert außerordentliche Geschehnisse im Zeitbereich sowie Phasenkopplungen im Frequenzbereich. <br /> <br /> Die gewonnenen Erkenntnisse werden auf das Problem der Polbewegung angewendet. Die Hypothese einer nichtlinearen Beziehung zwischen der atmosphärischen Erregung und der Polbewegung wird untersucht. Eine nichtlineare Behandlung wird nicht für nötig gehalten. / In the nonlinear data analysis there is a popular Monte Carlo Test method due to Theiler (it was established about 10 years ago), the Theiler surrogate method, which tests whether a time series is of a linear origin. This method is being criticized, modified and generalized in this thesis. What Theiler wants to test, needs other surrogate methods, which are constructed here. And what Theiler really tests, does not need Monte Carlo methods. With the help of the concept of the phase signal, that is introduced here, other test options are possible. The phase signal helps also in investigating the relations between the nonlinear characteristics of the time series and their phase spectrum. The phase signal is derived from the phase spectrum of the time series and registers extraordinary events in the time domain as well as phase couplings in the frequency domain. <br /> <br /> These theoretical approches are applied to the problem of polar motion. The hypothesis of a nonlinear relationship between the atmospheric excitation and the pole movement is examined. A nonlinear treatment is not considered necessary.