Optimal design of orders of DFrFTs for sparse representations

This study proposes an optimal design of the orders of the discrete fractional Fourier transforms (DFrFTs) and construct an overcomplete transform using the DFrFTs with these orders for performing the sparse representations. The design problem is formulated as an optimisation problem with an -norm non-convex objective function. To avoid all the orders of the DFrFTs to be the same, the exclusive OR of two constraints are imposed. The constrained...