Engin Cemal Menguc

Lyapunov Stability Theory Based Adaptive Filter Algorithm for Noisy Measurements

This paper presents a Lyapunov stability theory based adaptive filter algorithm with a determined step size. The proposed algorithm thanks to its step size leads to a faster convergence rate and a lover misadjustment error in case of the noisy measurement environments. Also the proposed algorithm ensures to estimate the best optimal unknown weight vector by using a step size. Simulations on white and non-white Gaussian input signals justify the proposed algorithm for the noisy environments. The simulation results demonstrate good tracking capability and low misalignment error of the proposed algorithm in case of the noisy measurement environments for system identification problems.

A novel adaptive filter algorithm for tracking of chaotic time series

In this study, a novel tracking filter algorithm is proposed satisfying stability in the sense of Lyapunov and is performed which is independent of statistical properties of input. The robustness of the proposed filter is presented by using two benchmark chaotic time series found in the literature. The proposed filter is compared with well known classical filters and performed in a high performance.

Complex-valued least mean Kurtosis adaptive filter algorithm

In this study, a complex-valued least mean Kurtosis (CLMK) adaptive filter algorithm is designed for processing complex-valued signals. The performance of the designed algorithm is tested on a complex-valued system identification and compared the complex-valued least mean square (CLMS) and complex-valued normalized least mean square (CNLMS) algorithms. As a result, the CLMK algorithm shows a higher performance than the other algorithms in terms of the convergence rate, mean square error (MSE) and mean square deviation (MSD).

Lyapunov stability theory based complex valued adaptive filter design

In this study, a novel complex valued adaptive filter algorithm is proposed satisfying stability in the sense of Lyapunov. The prediction capability of the proposed algorithm is presented by using complex valued autoregressive process and wind signal in the literature. The proposed complex valued adaptive filter algorithm is compared with standard complex normalized least mean square algorithm and performed in a high performance.

A new approach to channel equalization problem

In this study, a new approach based on Lyapunov stability theory (LST) is proposed for channel equalization problem. For the first time, the convergence capability of the proposed algorithm is presented on the channel equalization problem. The proposed approach is compared with normalized least mean square (NLMS) algorithm. Simulation results show that the convergence capability of the proposed algorithm is better than NLMS algorithm. As a result, the proposed approach can effectively be used for the channel equalization problem.

A complex-valued adaptive filter algorithm for system identification problem

In this study, a complex-valued adaptive filter algorithm based on Lyapunov stability theory is presented to solve a system identification problem in the complex domain. The performance of the proposed complex-valued Lyapunov adaptive filter (CLAF) algorithm is improved for the complex-valued system identification problem by integrating the LST into the filter optimization cost. The performance of the proposed algorithm is tested on a complex-valued moving average (MA) system identification problem and compared with the conventional complex-valued least mean square (CLMS) and complex-valued normalized least mean square (CNLMS) algorithms. The simulation results show that the proposed CLAF algorithm has achieved a faster convergence rate and a lower steady-state MSE performance when compared to the other algorithms.

A new approach to adaptive noise cancellation in synthetic auditory evoked potentials

This paper presents a new approach for enhancing Auditory Evoked Potentials (AEP). In this study, we first generated synthetic single trial AEP data at some specified noise levels by using gamma-tone function technique and then applied the proposed Lyapunov theory based filter to the noisy AEP synthetic data. Simulation results have been demonstrated that enhanced AEP with LST based adaptive filter can effectively be used to cancel out background EEG noise for a better measurement.

Frequency Estimation Methods for Smart Grid Systems

Frequency is one of the most significant parameters in the smart grid systems. Thus, accurate frequency estimation becomes an essential task for monitoring, controlling and protecting a real-time smart grid system. In this chapter, we present an overview of the frequency estimation methods in the smart grid system with a focus on real-time adaptive estimation algorithms. Primarily, in Sects. 5.1 and 5.2, the importance of the frequency estimation in the smart grid systems and the challenges encountered in its real-time applications are introduced in detail. In Sect. 5.3, a three-phase power system is then formulated as a two-phase system in the complex domain by using the well-known Clarke’s transformation so as to be able to estimate the frequency of the smart grid system in the real time. For this purpose, the adaptive real-time frequency estimation algorithms are comparatively presented as strictly and widely linear algorithms in Sect. 5.4. The strictly linear algorithms yield optimal solutions only under balanced three-phase systems, whereas the widely linear algorithms give a better solution under both balanced and unbalanced conditions due to the fact that they take into account all statistical information of the system. Considering smart grid applications in real time, the mentioned properties of these algorithms under both balanced and unbalanced conditions are proven in Sect. 5.5.

An Augmented Complex-Valued Least-Mean Kurtosis Algorithm for the Filtering of Noncircular Signals

In this paper, a novel augmented complex-valued least-mean kurtosis (ACLMK) algorithm is proposed for processing complex-valued signals. The negated kurtosis of the complex-valued error signal is defined as a cost function by using augmented statistics. As a result of the minimization of this cost function, the ACLMK algorithm containing all second-order statistical properties is obtained for processing noncircular complex-valued signals. Moreover, in this paper, convergence and misadjustment conditions of the proposed ACLMK algorithm are derived from the steady-state analysis. The simulation results on complex-valued system identification, prediction, and adaptive noise cancelling problems show that the use of the cost function defined by the negated kurtosis of the complex-valued error signal based on augmented statistics enables the processing of the noncircular complex-valued signals, and significantly improves the performance of the proposed ACLMK algorithm in terms of the mean square deviation, the mean square error, the prediction gain and the convergence rate when compared to other algorithms.

Prediction of complex-valued signals by using complex-valued LMK algorithm

In this study, the adaptive prediction of complex-valued signals has been realized by using the complex-valued least mean Kurtosis (CLMK) algorithm. The prediction performance of the CLMK algorithm has been evaluated on three benchmark complex-valued signals and a complex-valued real-world radar data by comparing with the traditional least mean square (CLMS) algorithm. Simulation results have verified that the CLMK algorithm outperforms the CLMS algorithm.