Frequency domain quaternion adaptive filters: Algorithms and convergence performance

Recently, adaptive filtering was extended to quaternion-valued systems. Quaternion-valued algorithms exhibit improved geometrical properties compared with real- and complex-valued algorithms. Moreover, working in the frequency domain allows a fast execution along with a good convergence performance. In this work, we propose three different quaternion-valued adaptive algorithms operating in the frequency domain. Convergence properties are also analyzed: in particular, the step size stability range is obtained in relation to the eigenvalues of the input autocorrelation matrix and the Excess Mean Square Error (EMSE) is expressed in relation to the algorithm parameters. Finally, simulations support the proposal.