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Browsing DSP Publications by Author "Aravena, Jorge.L."
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Item Detecting Periodic Behavior in Nonstationary Signals(1998-10-20) Venkatachalam, Vidya; Aravena, Jorge.L.; Digital Signal Processing (http://dsp.rice.edu/)This paper presents results on the multiresolution analysis of nonstationary signals with the objective of detecting underlying periodic phenomena. Wavelet packet analysis with coefficient thresholding is the basis for the detection. The effectiveness of the method is illustrated by analyzing experimental data on sediment electrochemical redox potential in a tidal microcosm. The significance of the technique is that it can extract periodic phenomena from experimental data corrupted by catastrophic and random events, provide a signature of the basic periodic component, an give an estimate of the degree of deviation from periodic behavior. Consequently, it has potential applications in the analysis of quasi-periodic signals such as electrocardiograms (ECGs), where the determination of the extent of quasi-periodicity is of critical importance.Item Enhanced Pseudo Power Signatures for Nonstationary Signal Classification: The Projector Approach(1999-05-01) Venkatachalam, Vidya; Aravena, Jorge.L.; Digital Signal Processing (http://dsp.rice.edu/)The classification of nonstationary signals of unknown duration is of great importance in areas like oil exploration, moving target detection, and pattern recognition. In an earlier work, we provided a solution to this problem, based on the wavelet transform, by defining representations called pseudo power signatures for signal classes which were independent of signal length, location and magnitude, and proposed a simple approach using the Singular Value Decomposition to generate these signatures. This paper offers a new approach resulting in more discriminating signatures. The enhanced signatures are obtained by solving a nonlinear minimization problem involving an inverse projection. The problem formulation, solution procedure, and computational algorithm are presented in this work. An analysis of the projection signatures, and their efficacy in separating highly correlated signal classes are demonstrated through simulation examples.Item Enhanced signatures for event classification: The projector approach(1998-10-01) Venkatachalam, Vidya; Aravena, Jorge.L.; Digital Signal Processing (http://dsp.rice.edu/)The classification of nonstationary signals of unknown duration is of great importance in areas like oil exploration, moving target detection, and pattern recognition. In an earlier work, we provided a solution to this problem, based on the wavelet transform, by defining representations called pseudo power signatures for signal classes which were independent of signal length, and proposed a simple approach using the Singular Value Decomposition to generate these signatures. This paper offers a new approach resulting in more discriminating signatures. The enhanced signatures are obtained by solving a nonlinear minimization problem involving an inverse projection. The problem formulation, solution procedure, and computational algorithm are presented in this work. The efficacy of the projection signatures in separating highly correlated signal classes is demonstrated through a simulation example.Item Nonstationary signal classification using pseudo power signatures(1998-06-20) Venkatachalam, Vidya; Aravena, Jorge.L.; Digital Signal Processing (http://dsp.rice.edu/)This paper deals with the problem of classification of nonstationary signals using signatures which are essentially independent of the signal length. We develop the notion of a separable approximation to the Continuous Wavelet Transform (CWT) and use it to define a power signature. We present a simple technique which uses the Singular Value Decomposition (SVD) to compute such an approximation, and demonstrate through an example how it is used to perform the classification process. This example serves to show both the effectiveness and limitations of the approach. Our main result is an alternate approach which develops the idea of using orthogonal projections to refine the approximation process, thus allowing for the definition of better signatures.Item Nonstationary signal classification using pseudo power signatures: The Matrix SVD Approach(1999-12-20) Aravena, Jorge.L.; Venkatachalam, Vidya; Digital Signal Processing (http://dsp.rice.edu/)This paper deals with the problem of classification of nonstationary signals using signatures which are essentially independent of the signal length. This independence is a requirement in common classification problems like stratigraphic analysis, which was a motivation for this research. We achieve this objective by developing the notion of an approximation to the Continuous Wavelet Transform (CWT), which is separable in the time and scale parameters, and using it to define power signatures, which essentially characterize the scale energy density, independent of time. We present a simple technique which uses the Singular Value Decomposition (SVD) to compute such an approximation, and demonstrate through an example how it is used to perform the classification process. The proposed classification approach has potential applications in areas like moving target detection, object recognition, oil exploration, and speech processing.Item Nonstationary Signal Enhancement Using The Wavelet Transform(1996-03-20) Venkatachalam, Vidya; Aravena, Jorge.L.; Digital Signal Processing (http://dsp.rice.edu/)Conventional signal processing typically involves frequency selective techniques which are highly inadequate for nonstationary signals. In this paper, we present an approach to perform time-frequency selective processing using the Wavelet Transform. The approach is motivated by the excellent localization, in both time and frequency, afforded by the wavelet basis functions. Suitably chosen wavelet basis functions are used to characterize the subspace of signals that have a given localized time-frequency support, thus enabling a time-frequency partitioning of signals. A practical implementation scheme using filter banks is also presented, and the effectiveness of the approach over conventional techniques is demonstrated.Item Optimal parallel 2-D FIR digital filter with separable terms(1997-05-01) Venkatachalam, Vidya; Aravena, Jorge.L.; Digital Signal Processing (http://dsp.rice.edu/)This paper completely solves the optimal Weighted Least Mean Square (WLMS) design problem using sums of separable terms. For any fixed number of separable terms (less than or equal to the rank of the unconstrained solution), the problem is solved as a sequence of separable filter approximations. An efficient computational algorithm based on necessary conditions is presented. The procedure allows a high degree of flexibility in the choice of filter orders and the number of separable terms, but it may converge to a local minimum. An improved approximation can be obtained by computing more terms than required and then performing a truncation of the coefficient matrix using a singular value analysis. A significant computational advantage is that the procedure requires neither the solution of the unconstrained WLMS problem nor the singular value analysis of the ideal filter.Item Pseudo Power Scale Signatures: Frequency Domain Approach(2000-03-01) Venkatachalam, Vidya; Aravena, Jorge.L.; Digital Signal Processing (http://dsp.rice.edu/)In an earlier work, we introduced a new form of signal representation called the pseudo power signature (PPS) that was essentially independent of the duration of the signal. The signatures were obtained based on the continuous wavelet transform, and were shown to be reliable and discriminating for classification purposes. In this paper, we take a fresh look at the problem of obtaining PPS by carrying out our analysis in the frequency domain. The main advantages of this approach over our earlier one, are that it is more versatile, permits the development of efficient computational algorithms, offers a solution to some unresolved uniqueness problems in our original formulation, and allows the study of the effect of the choice of analyzing wavelet to better aid the classification process.