Ta-Hsin Li

Blind identification and deconvolution of linear systems driven by binary random sequences

The problem of blind identification and deconvolution of linear systems with independent binary inputs is addressed. To solve the problem, a linear system is applied to the observed data and adjusted so as to produce binary outputs. It is proved that the system coincides with the inverse of the unknown system (with scale and shift ambiguities), whether it is minimum or nonminimum phase. These results are derived for nonstationary independent binary inputs of infinite or finite length. Based on these results, an identification method is proposed for parametric linear systems. It is shown that under some mild conditions, a consistent estimator of the parameter can be obtained by minimizing a binariness criterion for the output data. Unlike many other blind identification and deconvolution methods, this criterion handles nonstationary signals and does not utilize any moment information of the inputs. Three numerical examples are presented to demonstrate the effectiveness of the proposed method. >

Iterative filtering for multiple frequency estimation

It is well-known that Pronys least-squares estimator gives inconsistent estimates for multiple frequency estimation. In a recent attempt to diminish this problem, Dragosevic and Stankovic (1989) couple the least-squares method of autoregressive (AR) estimation with an iterative filtering scheme discussed by Kay (1988) using an all-pole filter. But the inconsistency still persists. This paper attacks the chronic inconsistency with a general approach of parametric filtering that unifies and extends the previous work. It is shown that the inconsistency can be eliminated with an appropriately parametrized filter. The clue for the correct parametrization comes from a formula for the bias of the least squares AR estimator. The fact of the matter is that as long as a filter satisfies the parametrization requirement, consistent estimates can be obtained from the least-squares AR estimator on the basis of the filtered data. In particular, the all-pole filter considered by Dragosevic and Stankovic can be easily reparametrized so that it too satisfies the parametrization requirement and thus leads to a consistent estimator. Experimental results show that the modified method has a higher resolution than the discrete Fourier transform and that its overall performance is quite remarkable. >

Strong consistency of the contraction mapping method for frequency estimation

Some statistical properties in regard to the contraction mapping (CM) method are discussed. One of the requirements in this method is that the filter be parameterized to satisfy a certain fundamental property. The parameterization clearly depends on the normalized noise spectrum which theoretically has to be known or estimated a priori. If this information is available, one can first whiten the noise with a linear filter and then apply the CM method to the filtered data. In this way, the parameterization only needs to be done under the white noise assumption and filters like the AR(2) can be used by the CM method. In applications, however, prewhitening may not always be necessary. >

Asymptotic normality of sample autocovariances with an application in frequency estimation

The asymptotic normality of sample autocovariances is proved for time series with mixed-spectra, which extends the classical results of Bartlett for linear processes. It is also shown that the asymptotic normality remains valid after linear filtering, if the filter is strictly stable so that the end-point effect of finite sample can be ignored. The developed theory is then employed to establish the asymptotic normality of a recently proposed fast frequency estimation procedure.

Tracking abrupt frequency changes

This paper addresses the problem of accurate estimation and rapid adaptation of abrupt frequency changes from noisy sinusoidal signals. A two‐filter adaptive algorithm is proposed to achieve the seemingly contradictory objectives. This algorithm is derived from an iterative batch procedure that has been proved to yield consistent and asymptotically Gaussian estimates for constant‐frequency estimation. These properties provide a basis for the detection of abrupt changes in the time‐varying frequency. Combining the high accuracy of narrow‐band/long‐memory filtering with the high adaptability of wide‐band/short‐memory filtering, the two‐filter approach is particularly suitable for tracking time‐varying frequencies that can be approximately modeled as piecewise‐constant functions of time. Simulation results are reported that justify the viability of the method.

Time‐correlation analysis of nonstationary time series

This paper introduces a new graphical method of displaying the evolutionary correlation properties of nonstationary time series. The method, called time‐correlation analysis (TCA), summarizes the local correlation properties with a smooth and monotone characterization function interpretable as the first‐order autocorrelation coefficient. The TCA plot is constructed by plotting the discretized characterization function as time series. Issues concerning the range of the TCA plot are investigated in detail. Both simulated and real‐data examples are given to demonstrate the application and interpretation of the method.