Institute for Systems Research

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Author: search.filters.author.Kedem, BenjaminSubject: search.filters.subject.Communication

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    On Autocovariance Estimation for Discrete Spectrum Stationary Time Series
    (1993) Houdre, Christian; Kedem, Benjamin; ISR
    We provide a necessary and sufficient condition for the almost sure convergence and the strong consistency of the sample autocovariance of a discrete spectrum weakly stationary process. This also clarifies the estimation of the autocovariance function of a mixed spectrum weakly stationary processes.
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    Estimation of Multiple Sinusoids by Parametric Filtering
    (1992) Li, Ta-Hsin; Kedem, Benjamin; ISR
    The problem of estimating the frequencies of multiple sinusoids from noisy observations is addressed in this paper. A parametric filtering approach, called the PF method, is proposed that leads to a consistent estimator of the AR representation of the sinusoidal signal, given the number of sinusoids. It is accomplished by using an iterative procedure to a fixed-point of the parametrized least squares estimator (from the filtered data) that comprises a contraction mapping in the vicinity of the true AR parameter. Employing appropriate filters, this method is able to achieve the accuracy of the nonlinear least squares estimator, with much less computational complexity and initialization requirement. It can also be implemented adaptively (recursively) in order to track time-varying frequencies. In this way, the PF method provides a flexible and efficient procedure of frequency estimation. An example of the AR filter is investigated in detail to illustrate the performance of the PF method.
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    On the Contraction Mapping Method for Frequency Detection
    (1992) Kedem, Benjamin; Yakowitz, S.; ISR
    The contraction mapping method for frequency estimation in the presence of noise, identifies the cosine of the frequency to be detected as a fixed point of a certain correlation mapping. At its hear, the method provides a plan for automatic self tuning of parametric filters. A variant of the method, called the HK algorithm, produces recursive zero-crossing rates (normalized HOC sequences) that converge to the frequency of interest. A statistical explanation for the contraction mapping method as epitomized by the HK algorithm is provided when the HOC sequences are produced by bandpass filters. The outright consistency of the zero-crossing rate is not required. Examples show that the method performs quite remarkably.
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    Asymptotic Normality of the Contraction Mapping Estimator for Frequency Estimation
    (1992) Li, Ta-Hsin; Kedem, Benjamin; Yakowitz, S.; ISR
    This paper investigates the asymptotic distribution of the recently-proposed contraction mapping (CM) method for frequency estimation. Given a finite sample composed of a sinusoidal signal in additive noise, the CM method applies to the data a parametric filter that matches its parameter with the first-order autocorrelation of the filtered noise. The CM estimator is defined as the fixed-point of the parametrized first-order sample autocorrelation of the filtered data. In this paper, it is proved that under appropriate conditions, the CM estimator is asymptotically normal with a variance inversely related to the signal-to-noise ratio. A useful example of the AR(2) filter is discussed in detail to illustrate the performance of the CM method.