An algorithm for discrete fractional Hadamard transform

TL;DR

This paper introduces a new efficient algorithm for computing the discrete fractional Hadamard transform, significantly reducing computational complexity from quadratic to near-linear for data vectors of size N that is a power of two.

Contribution

The paper presents a novel algorithm that decreases the number of multiplications needed to compute the discrete fractional Hadamard transform from N^2 to N log_2 N.

Findings

Reduces computational complexity for the transform

Efficient for data sizes that are powers of two

Potentially faster processing in signal analysis applications

Abstract

We present a novel algorithm for calculating the discrete fractional Hadamard transform for data vectors whose size N is a power of two. A direct method for calculation of the discrete fractional Hadamard transform requires $N^2$ multiplications, while in proposed algorithm the number of real multiplications is reduced to $N$log$_2N$.