Browsing by Author "Goncalves, Paulo"
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Item Diverging moments and parameter estimation(2004-01-15) Goncalves, Paulo; Riedi, Rudolf H.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)Heavy tailed distributions enjoy increased popularity and become more readily applicable as the arsenal of analytical and numerical tools grows. They play key roles in modeling approaches in networking, finance, hydrology to name but a few. The tail parameter is of central importance as it governs both the existence of moments of positive order and the thickness of the tails of the distribution. Some of the best known tail estimators such as Koutrouvelis and Hill are either parametric or show lack in robustness or accuracy. This paper develops a shift and scale invariant, non-parametric estimator for both, upper and lower bounds for orders with finite moments. The estimator builds on the equivalence between tail behavior and the regularity of the characteristic function at the origin and achieves its goal by deriving a simplified wavelet analysis which is particularly suited to characteristic functions.Item Hybrid Linear / Bilinear Time-Scale Analysis(1999-01-01) Pasquier, Martin; Goncalves, Paulo; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)We introduce a new method for the time-scale analysis of non-stationary signals. Our work leverages the success of the "time-frequency distribution series / cross-term deleted representations" into the time-scale domain to match wide-band signals that are better modeled in terms of time shifts and scale changes than in terms of time and frequency shifts. Using a wavelet decomposition and the Bertrand time-scale distribution, we locally balance linearity and bilinearity in order to provide good resolution while suppressing troublesome interference components. The theory of frames provides a unifying perspective for cross-term deleted representations in general.Item Hybrid Linear/Bilinear Time-Scale Analysis(1996-06-01) Pasquier, Martin; Goncalves, Paulo; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)We introduce a new method for the time-scale analysis of nonstationary signals. Our work leverages the success of the â time-frequency distribution series/cross-term deleted representationsâ into the time-scale domain to match wide-band signals that are not well modeled in terms of time and frequency shifts. Using a wavelet decomposition and the Bertrand (see J. Math. Phys., vol.33, p.2515-27, 1992) time-scale distribution, we locally balance linearity and bilinearity in order to provide good resolution while suppressing troublesome interference components. The theory of frames provides a unifying perspective and leads us to insights into the cross-term deleted representations.Item Improved Type-Based Detection of Analog Signals(1997-04-01) Goncalves, Paulo; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)When applied to continuous-time observations, type-based detection strategies are limited by the necessity to crudely quantize each sample. To alleviate this problem, we smooth the types for both the training and observation data with a linear filter. This post-processing improves the detector performance significantly (error probabilities decrease by over a factor of three) without incurring a significant computational penalty. However this improvement depends on the amplitude distribution and on the quantizer's characteristics.Item Pseudo Affine Wigner Distributions(1996-05-01) Goncalves, Paulo; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)In this paper, we introduce a new set of tools for time-varying spectral analysis: the pseudo affine Wigner distributions. Based on the affine Wigner distributions of J. and P. Bertrand, these new time-scale distributions support efficient online operation at the same computational cost as the continuous wavelet transform. Moreover, they take advantage of the proportional bandwidth smoothing inherent in the sliding structure of their implementation to suppress cumbersome interference components. To formalize their place within the echelon of the affine class of time-scale distributions, we extend the definition of this class and introduce other natural generators.Item Pseudo Affine Wigner Distributions: Definition and Kernel Formulation(1998-06-01) Goncalves, Paulo; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)In this paper, we introduce a new set of tools for time-varying spectral analysis: the pseudo affine Wigner distributions. Based on the affine Wigner distributions of J. and P. Bertrand, these new time-scale distributions support efficient online operation at the same computational cost as the continuous wavelet transform. Moreover, they take advantage of the proportional bandwidth smoothing inherent in the sliding structure of their implementation to suppress cumbersome interference components. To formalize their place within the echelon of the affine class of time-scale distributions, we extend the definition of this class and introduce other natural generators.Item A Pseudo-Bertrand Distribution for Time-Scale Analysis(1996-03-01) Goncalves, Paulo; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Using the pseudo-Wigner time-frequency distribution as a guide, we derive two new time-scale representations, the pseudo-Bertrand and the smoothed pseudo-Bertrand distributions. Unlike the Bertrand distribution, these representations support efficient online operation at the same computational cost as the continuous wavelet transform. Moreover, they take advantage of the affine smoothing inherent in the sliding structure of their implementation to suppress cumbersome interference components.Item A Simple Statistical Analysis of Wavelet-based Multifractal Spectrum Estimation(1998-11-01) Goncalves, Paulo; Riedi, Rudolf H.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)The multifractal spectrum characterizes the scaling and singularity structures of signals and proves useful in numerous applications, from network traffic analysis to turbulence. Of great concern is the estimation of the spectrum from a finite data record. In this paper, we derive asymptotic expressions for the bias and variance of a wavelet-based estimator for a fractional Brownian motion (fBm) process. Numerous numerical simulations demonstrate the accuracy and utility of our results.Item Wavelet Analysis of Fractional Brownian Motion in Multifractal Time(1999-09-20) Goncalves, Paulo; Riedi, Rudolf H.; Digital Signal Processing (http://dsp.rice.edu/)We study fractional Brownian motions in multifractal time, a model for multifractal processes proposed recently in the context of economics. Our interest focuses on the statistical properties of the wavelet decomposition of these processes, such as residual correlations (LRD) and stationarity, which are instrumental towards computing the statistics of wavelet-based estimators of the multifractal spectrum.