A Statistical Perspective of the Empirical Mode Decomposition

This research focuses on non-stationary basis decompositions methods in time-frequency analysis. Classical methodologies in this field such as Fourier Analysis and Wavelet Transforms rely on strong assumptions of the underlying moment generating process, which, may not be valid in real data scenarios or modern applications of machine learning. The literature on non-stationary methods is still in its infancy, and the research contained in this thesis aims to address challenges arising in this area. Among several alternatives, this work is based on the method known as the Empirical Mode Decomposition (EMD). The EMD is a non-parametric time-series decomposition technique that produces a set of time-series functions denoted as Intrinsic Mode Functions (IMFs), which carry specific statistical properties. The main focus is providing a general and flexible family of basis extraction methods with minimal requirements compared to those within the Fourier or Wavelet techniques. This is highly important for two main reasons: first, more universal applications can be taken into account; secondly, the EMD has very little a priori knowledge of the process required to apply it, and as such, it can have greater generalisation properties in statistical applications across a wide array of applications and data types. The contributions of this work deal with several aspects of the decomposition. The first set regards the construction of an IMF from several perspectives: (1) achieving a semi-parametric representation of each basis; (2) extracting such semi-parametric functional forms in a computationally efficient and statistically robust framework. The EMD belongs to the class of path-based decompositions and, therefore, they are often not treated as a stochastic representation. (3) A major contribution involves the embedding of the deterministic pathwise decomposition framework into a formal stochastic process setting. One of the assumptions proper of the EMD construction is the requirement for a continuous function to apply the decomposition. In general, this may not be the case within many applications. (4) Various multi-kernel Gaussian Process formulations of the EMD will be proposed through the introduced stochastic embedding. Particularly, two different models will be proposed: one modelling the temporal mode of oscillations of the EMD and the other one capturing instantaneous frequencies location in specific frequency regions or bandwidths. (5) The construction of the second stochastic embedding will be achieved with an optimisation method called the cross-entropy method. Two formulations will be provided and explored in this regard. Application on speech time-series are explored to study such methodological extensions given that they are non-stationary

The 31st Aerospace Mechanisms Symposium

The proceedings of the 31st Aerospace Mechanisms Symposium are reported. Topics covered include: robotics, deployment mechanisms, bearings, actuators, scanners, boom and antenna release, and test equipment. A major focus is the reporting of problems and solutions associated with the development and flight certification of new mechanisms

Proceedings of the Nimbus Program Review

The Nimbus program review was conducted at the George Washington Motor Lodge and at General Electric Missiles and Space Division, Valley Forge, Pennsylvania, on November 14, 15, and 16, 1962. The purpose of the review was twofold: first, to present to top management of the Goddard Space Flight Center (GSFC), National Aeronautics and Space Administration (NASA) Headquarters, other NASA elements, Joint Meteorological Satellite Advisory Committee (_MSAC), Weather Bureau, subsystem contractors, and others, a clear picture of the Nimbus program, its organization, its past accomplishments, current status, and remaining work, emphasizing the continuing need and opportunity for major contributions by the industrial community; second, to bring together project and contractor technical personnel responsible for the planning, execution, and support of the integration and test of the spacecraft to be initiated at General Electric shortly. This book is a compilation of the papers presented during the review and also contains a list of those attending