Discrete Pseudo-Fractional Hadamard Transform and its Fast Algorithm

Abstract

In this paper a new discrete fractional transform for data vectors whose size $N$ is a power of two is proposed. The basic operation of the introduced transform is a discrete fractional Hadamard transform. Since the described transform is not a classical discrete fractional Hadamard transform in its pure form, we called it a pseudo-fractional discrete Hadamard transform. A generalization of the new transform is also defined so that it depends on many parameters. Fast algorithm for calculating the proposed transform is developed.