A novel time-series relationship among four consecutive real-valued single-tone sinusoid samples is proposed based on their linear prediction property. In order to achieve unbiased frequency estimates for a real sinusoid in white noise, based on the proposed four-point time-series relationship, a constrained least squares cost function is minimized based on the unit-norm principle. Closed-form expressions for the variance and the asymptotic expression for the variance of the proposed frequency estimator are derived, facilitating a theoretical performance comparison with the existing three-point counterpart, called as the reformed Pisarenko harmonic decomposer (RPHD). The region of performance advantage of the proposed four-point based constrained least squares frequency estimator over the RPHD is also discussed. Computer simulations are conducted to support our theoretical development and to compare the proposed estimator performance with the RPHD as well as the Cramer-Rao lower bound (CRLB).

Variance analysis is an important research topic to assess the quality of estimators. In this paper, we analyze the performance of the least ℓp-norm estimator in the presence of mixture of generalized Gaussian (MGG) noise. In the case of known density parameters, the variance expression of the ℓp-norm minimizer is first derived, for the general complex-valued signal model. Since the formula is a function of p, the optimal value of p corresponding to the minimum variance is then investigated. Simulation results show the correctness of our study and the near-optimality of the ℓp-norm minimizer compared with Cramér-Rao lower bound.

Boundary-based corner detection has been widely applied in spline curve fitting, automated optical inspection, image segmentation, object recognition, etc. In order to obtain good results, users usually need to adjust the length of region of support to resist zigzags due to quantization and random noise on digital boundaries. To automatically determine the length of region of support for corner detection, Teh-Chin and Guru-Dinesh presented adaptive approaches based on some local properties of boundary points. However, these local-property based approaches are sensitive to noise. In this paper, we propose a new approach to find the optimum length of region of support for corner detection based on a statistic discriminant criterion. Since our approach is based on the global perspective of all boundary points, rather than the local properties of some points, the experiments show that the determined length of region of support increases as the noise intensity strengthens. In addition, the detected corners based on the optimum length of region of support are consistent with human experts' judgment, even for noisy boundaries.

IC performance simulation for statistical purpose is usually very time-consuming since the scale and complexity of IC have increased greatly in recent years. A common approach for reduction of simulation cost is aimed at the nature of simple modeling instead of actual circuit performance simulations. In this paper,a stochastic interpolation model (SIM) scheme is proposed which overcomes the drawbacks of the existing polynomial-based approximation schemes. First,the dependence of the R2press statistic upon a parameter in SIM is taken into account and by maximizing R2press this enables SIM to achieve the best approximation accuracy in the given sample points without any assumption on the sample data. Next, a sequential sampling strategy based on variance analysis is described to effectively construct SIM during its update process. In each update step, a new sample point with a maximal value of variance is added to the former set of the sample points. The update process will be continued until the desired approximation accuracy is reached. This would eventually lead to the realization of SIM with a quite small number of sample points. Finally, the coefficient of variance is introduced as another criterion for approximation accuracy check other than the R2press statistic. The effectiveness of presented implementation scheme is demonstrated by several numerical examples as well as a statistical circuit analysis example.