Computing autocorrelation coefficient can effectively reduce the influence of additive white noise, thus estimation precision will be improved. In this paper, an autocorrelation-like function, different from the ordinary one, is defined, and is proven to own better linear predictive performance. Two algorithms for signal model are developed to achieve frequency estimates. We analyze the theoretical properties of the algorithms in the additive white Gaussian noise. The simulation results match with the theoretical values well in the sense of mean square error. The proposed algorithms compare with existing estimators, are closer to the Cramer-Rao bound (CRLB). In addition, computer simulations demonstrate that the proposed algorithms provide high accuracy and good anti-noise capability.

The optimal design of an extrapolated impulse response (EIR) filter (in the mini-max sense) is a non-linear programming problem. In this paper, the optimal design of the EIR filter by the semi-infinite programming (SIP) is investigated and an iterative technique for optimally designing the EIR filter is proposed. The simulation experiment validates the effectiveness of the SIP technique and the proposed iterative technique in the optimal design of the EIR filter.

In this paper, an iterative optimal method is proposed to design the prototype filters for a fast filter bank (FFB) with low complexity, aiming to control the optimum ripple magnitude tolerance of each filter according to the overall specifications. This problem is formulated as an optimization problem for which the total number of multiplications is to be minimized subject to the constrained ripple in the passband and stopband. In the following, an iterative solution is proposed to solve this optimization problem for the purpose of obtaining the impulse response coefficients with low complexity at each stage. Simulations are conducted to verify the performance of the proposed scheme and show that compared with the original method, the proposed scheme can reduce about 24.24% of multiplications. In addition, the proposed scheme and the original method provide similar mean square error (MSE) and the mean absolute error (MAE) of the frequency response.

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).