Design of Hilbert transformer and digital differentiator using a neural learning algorithm

This paper proposes a neural-based learning approach for the design of digital differentiator and Hilbert transformer. The error differences in the frequency domain are formulated as an eigenproblem such that the optimal filter is derived by solving a single eigenvector corresponding to the smallest eigenvalue of an appropriate real, symmetric, and positive-definite matrix. In this paper, the minor component analysis based neural approach is applied to the eigenfilter design with effectiveness. As the learning algorithm achieves convergence, the weight vector of the neuron would approach to the eigenvector which results the optimal filter coefficients of eigenfilter design. Simulation results indicate that the proposed neural learning approach can implement the eigenfilter design with good performance.