Analysis and Evaluation of the Family of Sign Adaptive Algorithms

In this thesis, four novel sign adaptive algorithms proposed by the author were analyzed and evaluated for floating-point arithmetic operations. These four algorithms include Sign Regressor Least Mean Fourth (SRLMF), Sign Regressor Least Mean Mixed-Norm (SRLMMN), Normalized Sign Regressor Least Mean Fourth (NSRLMF), and Normalized Sign Regressor Least Mean Mixed-Norm (NSRLMMN). The performance of the latter three algorithms has been analyzed and evaluated for real-valued data only. While the performance of the SRLMF algorithm has been analyzed and evaluated for both cases of real- and complex-valued data. Additionally, four sign adaptive algorithms proposed by other researchers were also analyzed and evaluated for floating-point arithmetic operations. These four algorithms include Sign Regressor Least Mean Square (SRLMS), Sign-Sign Least Mean Square (SSLMS), Normalized Sign-Error Least Mean Square (NSLMS), and Normalized Sign Regressor Least Mean Square (NSRLMS). The performance of the latter three algorithms has been analyzed and evaluated for both cases of real- and complex-valued data. While the performance of the SRLMS algorithm has been analyzed and evaluated for complex-valued data only. The framework employed in this thesis relies on energy conservation approach. The energy conservation framework has been applied uniformly for the evaluation of the performance of the aforementioned eight sign adaptive algorithms proposed by the author and other researchers. In other words, the energy conservation framework stands out as a common theme that runs throughout the treatment of the performance of the aforementioned eight algorithms. Some of the results from the performance evaluation of the four novel sign adaptive algorithms proposed by the author, namely SRLMF, SRLMMN, NSRLMF, and NSRLMMN are as follows. It was shown that the convergence performance of the SRLMF and SRLMMN algorithms for real-valued data was similar to those of the Least Mean Fourth (LMF) and Least Mean Mixed-Norm (LMMN) algorithms, respectively. Moreover, it was also shown that the NSRLMF and NSRLMMN algorithms exhibit a compromised convergence performance for realvalued data as compared to the Normalized Least Mean Fourth (NLMF) and Normalized Least Mean Mixed-Norm (NLMMN) algorithms, respectively. Some misconceptions among biomedical signal processing researchers concerning the implementation of adaptive noise cancelers using the Sign-Error Least Mean Fourth (SLMF), Sign-Sign Least Mean Fourth (SSLMF), and their variant algorithms were also removed. Finally, three of the novel sign adaptive algorithms proposed by the author, namely SRLMF, SRLMMN, and NSRLMF have been successfully employed by other researchers and the author in applications ranging from power quality improvement in the distribution system and multiple artifacts removal from various physiological signals such as ElectroCardioGram (ECG) and ElectroEncephaloGram (EEG)

Analysis of the sign regressor least mean fourth adaptive algorithm

A novel algorithm, called the signed regressor least mean fourth (SRLMF) adaptive algorithm, that reduces the computational cost and complexity while maintaining good performance is presented. Expressions are derived for the steady-state excess-mean-square error (EMSE) of the SRLMF algorithm in a stationary environment. A sufficient condition for the convergence in the mean of the SRLMF algorithm is derived. Also, expressions are obtained for the tracking EMSE of the SRLMF algorithm in a nonstationary environment, and consequently an optimum value of the step-size is obtained. Moreover, the weighted variance relation has been extended in order to derive expressions for the mean-square error (MSE) and the mean-square deviation (MSD) of the proposed algorithm during the transient phase. Computer simulations are carried out to corroborate the theoretical findings. It is shown that there is a good match between the theoretical and simulated results. It is also shown that the SRLMF algorithm has no performance degradation when compared with the least mean fourth (LMF) algorithm. The results in this study emphasize the usefulness of this algorithm in applications requiring reduced implementation costs for which the LMF algorithm is too complex

Removal of multiple artifacts from ECG signal using cascaded multistage adaptive noise cancellers

Although cascaded multistage adaptive noise cancellers have been employed before by researchers for multiple artifact removal from the ElectroCardioGram (ECG) signal, they all used the same adaptive algorithm in all the cascaded multi-stages for adjusting the adaptive filter weights. In this paper, we propose a cascaded 4-stage adaptive noise canceller for the removal of four artifacts present in the ECG signal, viz. baseline wander, motion artifacts, muscle artifacts, and 60 Hz Power Line Interference (PLI). We have investigated the performance of eight adaptive algorithms, viz. Least Mean Square (LMS), Least Mean Fourth (LMF), Least Mean Mixed-Norm (LMMN), Sign Regressor Least Mean Square (SRLMS), Sign Error Least Mean Square (SELMS), Sign-Sign Least Mean Square (SSLMS), Sign Regressor Least Mean Fourth (SRLMF), and Sign Regressor Least Mean Mixed-Norm (SRLMMN) in terms of Signal-to-Noise Ratio (SNR) improvement for removing the aforementioned four artifacts from the ECG signal. We employed the LMMN, LMF, LMMN, LMF algorithms in the proposed cascaded 4-stage adaptive noise canceller to remove the respective ECG artifacts as mentioned above. We succeeded in achieving an SNR improvement of 12.7319 dBs. The proposed cascaded 4-stage adaptive noise canceller employing the LMMN, LMF, LMMN, LMF algorithms outperforms those that employ the same algorithm in the four stages. One unique and powerful feature of our proposed cascaded 4-stage adaptive noise canceller is that it employs only those adaptive algorithms in the four stages, which are shown to be effective in removing the respective ECG artifacts as mentioned above. Such a scheme has not been investigated before in the literature

Specifying the Forecast Generating Process for Exchange Rate Survey Forecasts

This paper contributes to the literature on the modeling of survey forecasts using learning variables. We use individual industry data on yen-dollar exchange rate predictions at the two week, three month, and six month horizons supplied by the Japan Center for International Finance. Compared to earlier studies, our focus is not on testing a single type of learning model, whether univariate or mixed, but on searching over many types of learning models to determine if any are congruent. In addition to including the standard expectational variables (adaptive, extrapolative, and regressive), we also include a set of interactive variables which allow for lagged dependence of one industry’s forecast on the others. Our search produces a remarkably small number of congruent specifications-even when we allow for 1) a flexible lag specification, 2) endogenous break points and 3) an expansion of the initial list of regressors to include lagged dependent variables and use a General-to-Specific modeling strategy. We conclude that, regardless of forecasters’ ability to produce rational forecasts, they are not only “different,” but different in ways that cannot be adequately represented by learning models.Learning Models, Exchange Rate, Survey Forecasts

A Unifying Approach to Quaternion Adaptive Filtering: Addressing the Gradient and Convergence

A novel framework for a unifying treatment of quaternion valued adaptive filtering algorithms is introduced. This is achieved based on a rigorous account of quaternion differentiability, the proposed I-gradient, and the use of augmented quaternion statistics to account for real world data with noncircular probability distributions. We first provide an elegant solution for the calculation of the gradient of real functions of quaternion variables (typical cost function), an issue that has so far prevented systematic development of quaternion adaptive filters. This makes it possible to unify the class of existing and proposed quaternion least mean square (QLMS) algorithms, and to illuminate their structural similarity. Next, in order to cater for both circular and noncircular data, the class of widely linear QLMS (WL-QLMS) algorithms is introduced and the subsequent convergence analysis unifies the treatment of strictly linear and widely linear filters, for both proper and improper sources. It is also shown that the proposed class of HR gradients allows us to resolve the uncertainty owing to the noncommutativity of quaternion products, while the involution gradient (I-gradient) provides generic extensions of the corresponding real- and complex-valued adaptive algorithms, at a reduced computational cost. Simulations in both the strictly linear and widely linear setting support the approach