Computation of an eigendecomposition-based discrete fractional Fourier transform with reduced arithmetic complexity

Abstract

In this paper, we introduce a method for computing an eigendecomposition-based discrete fractional Fourier transform (DFrFT) with reduced arithmetic complexity, when compared to the O(N2) complexity of the corresponding direct computation. Our approach exploits properties of a recently introduced closed-form Hermite-Gaussian-like discrete Fourier transform eigenbasis, which is used to define the DFrFT, and includes a rounding strategy. The proposed (exact) technique requires a slightly lower number of multiplications and half or less additions than what is required by other state-of-the-art methods; if the referred rounding strategy is applied, up to 65% of multiplications can be avoided. We validate our results by means of computer experiments where the application of the transform in signal filtering and compact representation is considered.