A New Fast Algorithm for Discrete Fractional Hadamard Transform

Abstract

This paper proposes a new fast algorithm for calculating the discrete fractional Hadamard transform for data vectors whose size $N$ is a power of two. A direct method for the calculation of the discrete fractional Hadamard transform requires $O(N^{2})$ multiplications, the last fast algorithm requires $O(N \log _{2}~N)$ , while in the proposed algorithm the number of multiplications is reduced to $O(N)$ .