Efficient Computation for Discrete Fractional Hadamard Transform

This paper introduces a new fast algorithm for the discrete fractional Hadamard transform (FHT). The proposed algorithm demonstrates superior computational efficiency. For data lengths ranging from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \leq N \leq 1024$ </tex-math></inline-formula>, our algorithm achieves a reduction in the number of multiplications by up to 96.53%, 81.82%, 33.33%, and 90% compared to four existing fast algorithms for the FHT. Additionally, we compare the execution times with those of existing fast algorithms, and the results show that the proposed algorithm has better performance. The reduced computational complexity makes the proposed algorithm a potential candidate for calculating the FHT.