Original structure for Walsh–Hadamard transform on sliding window

The Nth-order Walsh-Hadamard transform on a sliding window is described here by means of FIF filters. Factoring the transfer functions of the filters allows for a synthesis of the transform as a tree of comb filters. The trees built in ascending or descending order of the delay value allow the computation of the coefficients, respectively, in the sequency order and in the Hadamard order. The proposed algorithm requires 2N-2 additions for each projection. The resources used for a parallel field programmable gate array implementation are presented.