Hardware to compute Walsh coefficients

This paper presents a method to compute a fragment of the Walsh coefficients of logic functions using hardware. First, it introduces the Walsh transformation tree, and shows a method to compute Walsh coefficients using the Walsh transformation tree. Next, it shows the hardware realization for the Walsh tree. The amount of hardware to compute a coefficient and the entire coefficients are O(2ⁿ) and O(n²·2ⁿ), respectively. FPGA implementations show their feasibility up to n=14. The FPGA realization is at least 1253 times faster than a software implementation on a microprocessor for n=14.