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Onkar J Dabeer, Institute of Technology, Bombay (India)
Uday B Desai, Institute of Technology, Bombay (India)
In this paper a definition of multiresoltuion analysis (MRA) of Gaussian processes is proposed. The problem, in a natural way, reduces to the MRA of the associated reproducing kernel Hilbert space. We then show that for processes synthesized from Gaussian white process by fractional integration of order greater than 1, this definition is applicable. The MRA results in an orthogonal expansion of these processes. The region of interest is the positive real line. Using this representation then a decomposition of a wider class of Gaussian processes is given. This representation is multiscale in two ways : firstly, the Gaussian process is split into various component processes characterized by the smoothness of their sample paths and secondly,each of these component processes has a MRA as defined in this paper.
ic981102.pdf (From Postscript)
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Cedric Richard, Laboratoire LM2S, UTT (France)
Regis Lengelle, Laboratoire LM2S, UTT (France)
Detectors design requires substantial knowledge of the observation statistical properties, conditionally to the competing hypotheses H0 and H1. However, many applications involve complex phenomena, in which few a priori information is available. Several methods of designing time-frequency-based (TF) receivers from labeled training data have been proposed. Unfortunately, the resulting detectors have large biases, particularly when the number of training samples is small against the data dimension. The method presented here is based on the Structural Risk Minimization principle developed by Vapnik, and consists in locally adjusting the resolution of TF-based detectors to the information carried by each TF location. This operation, controlled by a measure of H0 and H1 separability, allows to advantageously reduce receivers complexity and solutions bias. The resulting reduced-bias TF-based detectors can yield a substantial improvement in detection performances.
ic981250.pdf (From Postscript) TOP
Syed I Shah, University of Pittsburgh (U.S.A.)
Luis F. Chaparro, University of Pittsburgh (U.S.A.)
Amro El-Jaroudi, University of Pittsburgh (U.S.A.)
We present a new technique for estimating the generalized transfer function (GTF) of a time-varying filter from time-frequency representations (TFRs) of its output. We use the fact that many of these representations can be written as blurred versions of the GTF. The approach consists in minimizing the error between the TFR found from the data and that found by blurring the GTF. The problem as such has many solutions. We, therefore, additionally constrain it to minimize the distance between the GTF-based spectrum and the autoterms of the Wigner distribution, suppressing the cross terms using an appropriate signal dependent mask function. To illustrate the performance of the proposed procedure we apply it to the spectral representation of speech and to signal masking and demonstrate its superior performance over the existing methods.
ic981758.pdf (From Postscript) TOP
Louis L. Scharf, University of Colorado, Boulder (U.S.A.)
Benjamin Friedlander, University of California, Davis (U.S.A.)
C. T. Mullis, University of Colorado, Boulder (U.S.A.)
Some quadratic time-frequency representations (TFRs) may be called time-varying spectrum estimators. They are derived from first principles, and they turn out to be time-varying multiwindow spectrum estimators. In special cases they are time-varying spectrograms that may be written as Fourier transforms of lag-windowed, time-varying correlation sequences or as spectrally smoothed time-varying periodograms. These are not ad-hoc variations on stationary ideas to accommodate time variation. Rather, they are the only variations one can obtain for time-varying spectrum analysis.
ic981760.pdf (Scanned) TOP
Ferhat Cakrak, University of Pittsburgh (U.S.A.)
Patrick J Loughlin, University of Pittsburgh (U.S.A.)
A non-linear multi-window method for generating a time-varying spectrum of non-stationary signals in noise is presented. The time-varying spectrum is computed from an optimally weighted average of multiple Hermite windowed spectrograms. The weights are determined using linear least squares estimation with respect to a reference time-frequency distribution. A masking operation is also used to reduce extraneous side lobes introduced by higher order Hermite windows. Several examples are provided, with performance criteria measures, to demonstrate and quantify the effectiveness of this new method.
ic982036.pdf (From Postscript) TOP
Thanh D Nguyen, Auburn University (U.S.A.)
Stanley J. Reeves, Auburn University (U.S.A.)
Thomas S Denney Jr, Auburn University (U.S.A.)
In this paper, we determine the optimal pulse shape for estimating positions of superimposed pulses by deriving the Cramer-Rao lower bound (CRLB) on the average estimation error variance and optimizing it with respect to pulse shape. Our results show that a significant improvement in estimation error variance can be achieved relative to Gaussian and rectangular pulse shapes.
ic982149.pdf (From Postscript) TOP
Andreas Jakobsson, Uppsala University (Sweden)
Arnold Lee Swindlehurst, Brigham Young University (U.S.A.)
Petre Stoica, Uppsala University (Sweden)
This paper considers the problem of estimating the time delays and doppler shifts of a known waveform received via several distinct paths by an array of antennas. The general maximum likelihood estimator is presented, and is shown to require a $2d$-dimensional non-linear minimization, where $d$ is the number of received signal reflections. Two alternative solutions based on signal and noise subspace fitting are proposed, requiring only a $d$-dimensional minimization. In particular, we show how to decouple the required search into a two-step procedure, where the delays are estimated and the dopplers solved for explicitly. Initial conditions for the time delay search can be obtained by applying generalizations of the MUSIC and ESPRIT algorithms.
ic982240.pdf (From Postscript) TOP
Mototsugu Abe, The University of Tokyo (Japan)
Shigeru Ando, The University of Tokyo (Japan)
This paper describes a new method for computational auditory scene analysis which is based on 1) waveform operators to extract instantaneous frequency (IF), frequency change (FM), and amplitude change (AM) from subband signals, and 2) a voting method into a probability distribution to extract coherency (shared fundamental frequency, shared FM, and shared AM) involved in them. We introduce non-parametric Kalman filtering for the time-axis integration. A consistent AM operator which is independent to frequency change is newly defined. Sharpness of the resultant probability distribution is examined with relating to the definition of the operators and subband bandwidth. We evaluate the performance of the algorithm by using several speech sounds.
ic982552.pdf (From Postscript) TOPJames W Pitton, MathSoft (U.S.A.)
This paper extends Thomson's multitaper spectrum estimation method to nonstationary signals. The method uses a newly-derived set of basis functions which generalize the concentration properties of the prolate spheroidal waveforms to the time-frequency case. We solve for the basis which diagonalizes the nonstationary spectrum generating operator over a finite region of the time--frequency plane. These eigenfunctions are maximally concentrated to and orthogonal over the specified time-frequency region, and are thus doubly orthogonal. Individual spectrograms computed with these eigenfunctions form direct time-frequency spectrum estimates. We next present a multitaper time-frequency spectrum estimation procedure using these time-frequency eigenestimates. Bias and variance expressions are derived, allowing for a statistical characterization of the accuracy of the estimate. The time-frequency concentration property of the basis functions yields an estimator with excellent bias properties, while the variance of the estimate is reduced through the use of multiple orthogonal windows.
ic982581.pdf (From Postscript) TOP
Osama A. Ahmed, King Fahd University of Petroleum & Minerals (Saudi Arabia)
Moustafa M. Fahmy, King Fahd University of Petroleum & Minerals (Saudi Arabia)
A new implementation of the critically sampled non-periodic real Gabor transform (GT) is presented for non-separable time-frequency (TF) plane sampling. In the proposed implementation, the quincunx sampling is used to sample the TF plane. This leads to a well localized biortogonal function in both time and frequency. It thus overcomes the main problem of the previous implementations, which is the non-localization of the resultant biorthogonal function. A fast algorithm to compute the derived biorthogonal function is proposed.
ic985056.pdf (Scanned) TOP