A new LMS algorithm for analysis of atrial fibrillation signals

Equations for normalization of x-axis and y-axis shift and scale are first derived. The algorithm is implemented for real-time analysis of CFAE acquired during atrial fibrillation (AF). Data was acquired at a 977？Hz sampling rate from 10 paroxysmal and 10 persistent AF patients undergoing clinical electrophysiologic study and catheter ablation therapy. Over 24 trials, normalization characteristics using the new algorithm with four weights were compared to the Widrow-Hoff LMS algorithm with four tapped delays. The time for convergence, and the mean squared error (MSE) after convergence, were compared. The new LMS algorithm was also applied to lead aVF of the electrocardiogram in one patient with longstanding persistent AF, to enhance the F wave and to monitor extrinsic changes in signal shape. The average waveform over a 25？s interval was used as a prototypical reference signal for matching with the aVF lead.Based on the derivation equations, the y-shift and y-scale adjustments of the new LMS algorithm were shown to be equivalent to the scalar form of the Widrow-Hoff LMS algorithm. For x-shift and x-scale adjustments, rather than implementing a long tapped delay as in Widrow-Hoff LMS, the new method uses only two weights. After convergence, the MSE for matching paroxysmal CFAE averaged 0.46？±？0.49μV2/sample for the new LMS algorithm versus 0.72？±？0.35μV2/sample for Widrow-Hoff LMS. The MSE for matching persistent CFAE averaged 0.55？±？0.95μV2/sample for the new LMS algorithm versus 0.62？±？0.55μV2/sample for Widrow-Hoff LMS. There were no significant differences in estimation error for paroxysmal versus persistent data. From all trials, the mean convergence time was approximately 1 second for both algorithms. The new LMS algorithm was useful to enhance the electrocardiogram F wave by subtraction of an adaptively weighted prototypical reference signal from the aVF lead. The extrinsic weighting over 25？s demonstrated that time-varying functions such as patient respiratio