A running Walsh-Hadamard transform algorithm and its application to isotropic quadratic filter implementation

Two problems associated with adaptive isotropic quadratic filters are the computational complexity and the speed of convergence. This paper presents a transform domain implementation scheme to solve these problems. A new implementation of the filter using the Walsh-Hadamard transform (WHT) is described. A running WHT (RWHT) algorithm is also proposed to reduce the computational cost. Theoretical analysis shows that the number of operations of the WHT implementation (using the RWHT) is considerably less than that of the direct implementation. The advantage of using the WHT implementation is illustrated by modelling a real nonlinear system. Results show that the WHT implementation converges significantly faster than the direct implementation.