Browsing by Author "Yakowitz, S."
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Asymptotic Normality of the Contraction Mapping Estimator for Frequency Estimation(1992) Li, Ta-Hsin; Kedem, Benjamin; Yakowitz, S.; ISRThis 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.Item On the Contraction Mapping Method for Frequency Detection(1992) Kedem, Benjamin; Yakowitz, S.; ISRThe 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.