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Wei Zhao, Rochester Institute of Technology (U.S.A.)
Raghuveer M Rao, Rochester Institute of Technology (U.S.A.)
In this paper we present a novel model for purely discrete-time self-similar processes and scale-invariant systems. The results developed are based on a new interpretation of the discrete-time scaling (equivalently dilation or contraction) operation which is defined through a mapping between discrete and continuous time. It is shown that it is possible to have continuous scaling factors through this operation even though the signal itself is discrete-time. We study both deterministic and stochastic discrete-time self-similar signals. We then derive the existence conditions of discrete-time deterministically self-similar signals with respect to some specific mappings. Finally, we discuss the construction of discrete-time linear scale-invariant (LSI) system and present results related to white noise driven system models of stochastic self-similar signals. Unlike continuous-time self-similar signals, it is possible to construct a wide class of non-trivial discrete-time self-similar signals.
ic981825.pdf (From Postscript)
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Mark J Coates, Cambridge University (U.K.)
Christophe Molina, Anglia University (U.K.)
William J. Fitzgerald, Cambridge University (U.K.)
Ideally, kernels used to generate bilinear time-frequency distributions (TFD) should be signal-dependent, and optimised independently at every location in the time-frequency (TF) plane. This poses an extremely severe computational burden. A compromise is proposed in this paper: time-varying kernels are optimised for specific regions in the time-frequency plane. The regions, designed to isolate separate components comprising the signal, are determined by modelling the TFD using a finite mixture model of Gaussian distributions. The parameters of the model are estimated using a combination of the expectation-maximisation algorithm and functional merging. The regional optimisation provides improved separation and resolution of closely-spaced components when compared to methods using a solely time-varying kernel, without incurring an overwhelming computational expense.
ic981710.pdf (From Postscript) TOPJean-Philippe Ovarlez, ONERA/DEMR (France)
In signal analysis, the joint estimation of the time-scale parameters which can affect a known signal (Doppler effect or scale effect, delay, ...) may be a problem of interest. An important result has shown that, even if the quality of the time delay estimation is classically given by the inverse spread of the signal spectral density, the quality of the scale estimation only depends on the inverse of the signal spread in Mellin space. This spread has a direct interpretation in the time-frequency plane and can be precisely estimated when duration, bandwidth and relative bandwidth of the signal are known. We propose here to develop two methods of optimum signal synthesis which minimize the variance of the estimates given by the Cramer-Rao lower bounds. The first method is based on the stationary phase principle, applied on frequency and Mellin spaces, which allows to construct signals with given autocorrelation functions in scale and time spaces. The second one is devoted to the construction of a frequency phase law depending on the mellin variable with the spreads in frequency and Mellin spaces related to the expected scale and time-delay resolutions.
ic981208.pdf (From Postscript) TOP
Ramdas Kumaresan, University of Rhode Island (U.S.A.)
Ashwin Rao, University of Rhode Island (U.S.A.)
An analytic signal permits unambiguous characterization of the phase and envelope of a real signal. But the analytic signal's phase-derivative i.e., the instantaneous frequency (IF) is typically a wild function and can take on values ranging from negative infinity to positive infinity. Fortunately, any analytic signal can be decomposed into a minimum phase (MinP)signal component and an all-phase (AllP) signal component. While the MinP signal's log-envelope and its phase form a Hilbert transform pair, the AllP signal has a positive definite instantaneous frequency (PIF), unlike that of the original analytic signal. We propose an elegant computational algorithm that separates the MinP and AllP components of the analytic signal. The envelope of the MinP component corresponds to the AM and the PIF of the AllP component corresponds to the positive FM.
ic981226.pdf (From Postscript) TOPFlemming Pedersen, Aalborg University (Denmark)
This paper presents and studies a time frquency distribution obtained from a Gabor expansion of a signal. The distribution is named the Positive Gabor Spectrogram, and is a new positive-like distribution with correct marginal distributions. Two side effects of correct marginals are non-additivity and time frequency fading. These are phenomena of a statistical correct distribution which do not agree with our intuitive expectation of a time frequency representaion.
ic981255.pdf (From Postscript) TOP
Christoph M Delfs, Universtität Karlsruhe (Germany)
Friedrich M Jondral, Universtität Karlsruhe (Germany)
The classification of transient time-varying signals is important for industrial, biomedical and military applications. The attack phase of piano sounds is used as an example for transient, time-varying signals in a real data application. Discrete Fourier transform and time-invariant wavelet packet based algorithms are used alternatively for feature extraction. The training set is used for determining an appropriate feature selection. A classifier checks whether the generated features are sufficient in order to identify the correct piano. Classification results are presented and discussed.
ic981205.pdf (From Postscript) TOP
Byeong-Gwan Iem, University of Rhode Island (U.S.A.)
Antonia Papandreou-Suppappola, University of Rhode Island (U.S.A.)
G. Faye Boudreaux-Bartels, University of Rhode Island (U.S.A.)
We propose the new Po-Weyl symbol to analyze system induced time shifts and scale changes on the input signal. This new Weyl symbol (WS) is useful in wideband signal analysis. We also propose new WS as tools for analyzing systems which produce dispersive frequency shifts on the signal. We obtain these generalized, frequency-shift covariant WS bywarping conventional, narrowband WS. Using the new, generalized WS, we provide a formulation for the Weyl correspondence for linear systems with instantaneous frequency characteristics matched to user specified characteristics. We also propose a new interpretation of linear signal transformations as weighted superpositions of non-linear frequency shifts on the signal. Application examples in signal analysis and detection demonstrate the advantages of our new results.
ic982028.pdf (From Postscript) TOPLeon Cohen, City University of New York, Hunter College (U.S.A.)
We generalize the Wiener-Khinchin theorem. A full generalization is presented where both the autocorrelation function and power spectral density are defined in terms of a general basis set. In addition, we present a partial generalization where the density is the Fourier transform of the autocorrelation function but the autocorrelation function is defined in terms of an arbitrary basis set. Both the deterministic and random cases are considered.
ic985122.pdf (Scanned) TOP
Jeffrey C O'Neill, Ecole Normale Superieure de Lyon (France)
William J Williams, University of Michigan (U.S.A.)
Cohen's class of time-frequency distributions for continuous signals has recently been to extended to discrete signals using both an axiomatic approach and an operator theory approach. In this paper, we investigate the formulation of several classical time-frequency distributions (Wigner, Rihaczek, Margenau-Hill, Page, Levin,Born-Jordan, spectrogram)in the discrete Cohen's classes. The main result of this paper concludes that there does not exist a formulation of the Wigner distribution in all of the discrete Cohen's classes.
ic981062.pdf (From Postscript) TOP
Jijun Yin, Drexel University (U.S.A.)
Athina P Petropulu, Drexel University (U.S.A.)
1/f^(beta)-type spectral behavior has received considerable attention in the past few years becauseit arises from a wide range of nature phenomena. By expressing a 1/f^(beta) process as a fractional integral of white noise, we show that, if (beta) <1, the process is stationary and follows an (alpha)-stable model, while if (beta) >1, the process has stationaryalpha-stable increments. We also provide closed form expressions for the relationship between (beta) and (alpha). The theoretical results are verified via real ultrasound data. Ultrasound breast data, or their increments, which appear to be 1/f^(beta), are shown to follow reasonably well the (alpha)-stable model.
ic982241.pdf (Scanned) TOP