Application of the Non-Hermitian Singular Spectrum Analysis to the exponential retrieval problem

We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients computed for index translated copies of an initial time series. For these matrices a generalized eigenvalue problem is solved. The initial signal is mapped into the basis of the generalized eigenvectors and phase portraits are consequently analyzed. Pattern recognition techniques could be applied to distinguish phase portraits related to the exponentials and noise. Each frequency is evaluated by unwrapping phases of the corresponding portrait, detecting potential wrapping events and estimation of the phase slope. Efficiency of the proposed and existing methods is compared on the set of examples, including the white Gaussian and auto-regressive model noise

Application of the Non-Hermitian Singular Spectrum Analysis to the Exponential Retrieval Problem

Introduction. In practical signal processing and its many applications, researchers and engineers try to find a number of harmonics and their frequencies in a time signal contaminated by noise. In this manuscript we propose a new approach to this problem. Aim. The main goal of this work is to embed the original time series into a set of multi-dimensional information vectors and then use shift-invariance properties of the exponentials. The information vectors are cast into a new basis where the exponentials could be separated from each other. Materials and methods. We derive a stable technique based on the singular value decomposition (SVD) of lagcovariance and cross-covariance matrices consisting of covariance coefficients computed for index translated copies of an original time series. For these matrices a generalized eigenvalue problem is solved. Results. The original time series is mapped into the basis of the generalized eigenvectors and then separated into components. The phase portrait of each component is analyzed by a pattern recognition technique to distinguish between the phase portraits related to exponentials constituting the signal and the noise. A component related to the exponential has a regular structure, its phase portrait resembles a unitary circle/arc. Any commonly used method could be then used to evaluate the frequency associated with the exponential. Conclusion. Efficiency of the proposed and existing methods is compared on the set of examples, including the white Gaussian and auto-regressive model noise. One of the significant benefits of the proposed approach is a way to distinguish false and true frequency estimates by the pattern recognition. Some automatization of the pattern recognition is completed by discarding noise-related components, associated with the eigenvectors that have a modulus less than a certain threshold.Introduction. In practical signal processing and its many applications, researchers and engineers try to find a number of harmonics and their frequencies in a time signal contaminated by noise. In this manuscript we propose a new approach to this problem. Aim. The main goal of this work is to embed the original time series into a set of multi-dimensional information vectors and then use shift-invariance properties of the exponentials. The information vectors are cast into a new basis where the exponentials could be separated from each other. Materials and methods. We derive a stable technique based on the singular value decomposition (SVD) of lagcovariance and cross-covariance matrices consisting of covariance coefficients computed for index translated copies of an original time series. For these matrices a generalized eigenvalue problem is solved. Results. The original time series is mapped into the basis of the generalized eigenvectors and then separated into components. The phase portrait of each component is analyzed by a pattern recognition technique to distinguish between the phase portraits related to exponentials constituting the signal and the noise. A component related to the exponential has a regular structure, its phase portrait resembles a unitary circle/arc. Any commonly used method could be then used to evaluate the frequency associated with the exponential. Conclusion. Efficiency of the proposed and existing methods is compared on the set of examples, including the white Gaussian and auto-regressive model noise. One of the significant benefits of the proposed approach is a way to distinguish false and true frequency estimates by the pattern recognition. Some automatization of the pattern recognition is completed by discarding noise-related components, associated with the eigenvectors that have a modulus less than a certain threshold

Operational modal analysis and continuous dynamic monitoring of footbridges

Tese de doutoramento. Engenharia Civil. Universidade do Porto. Faculdade de Engenharia. 201

Late time response analysis in UWB radar for concealed weapon detection : feasibility study

Remote detection of body-worn concealed weapons or explosives (CWE) is a field of ongoing research. In this Thesis the feasibility of CWE detection by using the UWB radar is explored. The CWE detection is based on the analysis of the Late Time Response (LTR) of the human which has been illuminated by the UWB signal. A specific set of LTR parameters characterizes the target signature. Therefore the existence of a CWE attached on the human body will influence the LTR characteristics and give the composite object i.e. human-CWE a different signature than the simple object i.e. human. The CWE detection methodology is verified by theoretical analysis, modelling and extensive laboratory experimentation. Investigation of the way the LTR parameters are influenced by the existence of the CWE signifies the differences of the LTR signature between the human and human-CWE. So the resolution of the differences in the LTR of a human with and without a CWE as the main objective of the research, are presented in the Thesis. The results verify that CWE detection with the use of LTR is feasible under the experimental conditions presented. Furthermore consideration of all possible detection scenarios is out of the scope of this Thesis.EThOS - Electronic Theses Online ServiceGBUnited Kingdo