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.