Quaternion adaptive line enhancer

The recovery of periodic signals from their noisy single channel mixtures has made wide use of the adaptive line enhancer (ALE). The ALE, however, is not designed for detection of two-(2-D) or three-dimensional (3-D) periodic signals such as tremor in an unconstrained hand motion. An ALE which can perform restoration of 3-D periodic signals is therefore required for such purposes. These signals may not exhibit periodicity in a single dimension. To address and solve this problem a quaternion adaptive line enhancer (QALE) is introduced in this paper for the first time which exploits the quaternion least mean square (QLMS) algorithm for the detection of 3-D (extendable to 4-D) periodic signals.