Hardware Architectures for Computing Eigendecomposition-Based Discrete Fractional Fourier Transforms with Reduced Arithmetic Complexity

The fractional Fourier transform (FrFT) is a useful mathematical tool for signal and image processing. In some applications, the eigendecomposition-based discrete FrFT (DFrFT) is suitable due to its properties of orthogonality, additivity, reversibility and approximation of continuous FrFT. Although recent studies have introduced reduced arithmetic complexity algorithms for DFrFT computation, which are attractive for real-time and low-power consumption practical scenarios, reliable hardware architectures in this context are gaps in the literature. In this paper, we present two hardware architectures based on the referred algorithms to obtain N-point DFrFT (N = 4L, L is a positive integer). We validate and compare the performance of such architectures by employing field-programmable gate array implementations, co-designed with an embedded hard processor unit. In particular, we carry out computer experiments where synthesis, error and latency analyses are performed, and consider an application related to compact signal representation.