CAF–FrFT: A center-affine-filter with fractional Fourier transform to reduce the cross-terms of Wigner distribution

•A method for applying a center-affine-filter (CAF) to the rotated version of the WD obtaining from the fractional Fourier transform has been proposed.•Mathematical relation of the proposed CAF–FrFT to the original CAF has been deduced.•The optimal rotation angle is estimated with the criterion of maximum amplitude.

As a popular time–frequency representation, the Wigner distribution (WD) enjoys its excellent property of highly concentrated auto-terms, but suffers from cross-term problem. To reduce the cross-terms, we propose a method to apply a center-affine-filter (CAF) to the rotated version of the WD obtaining from the fractional Fourier transform (FrFT). We call this method a center-affine-filter with the fractional Fourier transform (CAF–FrFT). Here the optimal rotation angle is obtained via the FrFT of a signal under the criterion of maximum amplitude. The simulations were conducted on two types of signals, namely, parallel signals, and non-parallel signals. Both the qualitative comparisons and the quantitative measures show that the proposed CAF–FrFT outperforms the original CAF method.