Pure Number Discrete Fractional Complex Hadamard Transform

This paper introduces a novel discrete fractional transform termed as pure number discrete fractional complex Hadamard transform (PN-FCHT). The proposed PN-FCHT offers three advantages over the traditional discrete fractional Hadamard transform (FHT). Firstly, the higher-order PN-FCHT matrix exhibits the Self-Kronecker product structure, which allows for the recursive generation from the $2\times 2$ core PN-FCHT matrix. Secondly, it possesses two important properties for computation, i.e. pure number property. Lastly, compared to existing state-of-the-art fast FHT algorithms, the PN-FCHT can reduce the transform multiplication computational complexity by up to 80% and this results in a more efficient hardware implementation.