This paper presents an approach to the realization of low-sensitivity second-order digital filters. In contrast to existing methods, which use amplitude sensitivity as a criterion, the proposed method uses pole sensitivity. Pole sensitivity is quite useful for evaluating and comparing the performance of various types of filters because it is not a function of frequency. The relation between pole sensitivity and amplitude sensitivity is clarified, and it is shown that the minimization of amplitude sensitivity is equivalent to that of absolute value of pole sensitivity. For the minimization of pole sensitivity, the denominator polynomial of a second-order transfer function is expressed in a general form including two multiplier coefficients and some arbitrary integer parameters. Under certain constraints on the range of the parameters, which limit the filter complexity, the values of the parameters are determined through an exclusive search such that the pole sensitivity is minimized. The optimum set of the parameters are fully dependent on the given specifications, i.e. locations of the poles. Therefore the z-plane can be partitioned into some regions, in each of which a single set of the parameters is chosen. The resultant map enables one to realize low-sensitivity digital filters having any given characteristics. Finally, two illustrative examples are included.

In this paper, we present a new signal frequency estimation method based on the sinusoidal additive synthesis model. In the proposed method, frequencies in both the signal and noise are estimated with several delay times by using an expanded linear prediction (LP) method, and assuming that the signal is stationary and noise is unstationary in short record length. Frequencies in the signal are extracted according to their dependence on different delays. The frequency estimation can be accomplished with short record length even in the case where the number of frequency components in the signal is unknown. And it is capable of estimating the frequencies of a signal in the presence of noise. Furthermore, the proposed method estimates the parameters with less computation and high estimation accuracy. Simulation results are provided to confirm the effectiveness of the proposed method. The comparison of estimation accuracy between the proposed method and the analysis by synthesis (ABS) method is shown with the corresponding Cramer-Rao lower bound. And the frequency resolution of this method is also shown.

It is well known that KT method proposed by R. Kumaresan and D. W. Tufts is used as a popular parameter estimation method of exponentially damped signal. It is based on linear backward-prediction method and singular value decomposition (SVD). However, it is difficult to estimate parameters correctly by KT method in the case when high noise exists in the signal. In this paper, we propose a parameter (frequency components and damping factors) estimation method to improve the performance of KT method under high noise. In our proposed method, we find the signal zero groups by calculating zeros with different data record lengths according to the combination of forward-prediction and backward-prediction, the mean value of the zeros in the signal zero groups are calculated to estimate the parameters of the signal. The proposed method can estimate parameters correctly and accurately even when high noise exists in the signal. Simulation results are shown to confirm the effectiveness of the proposed method.