Scaled Wigner distribution using fractional instantaneous autocorrelation

Abstract

The traditional Wigner distribution (WD) is extended to a novel one inspired by the definition of fractional bispectrum, giving rise to a scaled version with respect to the frequency variable, termed as the scaled Wigner distribution (SWD). A natural magnification effect characterized by a factor k on the frequency axis enables the SWD to have flexibility to be used in cross-term reduction. Some essential properties of this variation generalize very nicely and simply the classical results for the WD, and it enjoys a computational complexity in the order of O(kN2) comparable to O(N2) of the WD. The SWD does not use localization windows, but its resolutions depend on the factor k. Comparison of the detection performance (i.e. cross-term reduction, time–frequency resolution, angle or distance resolution) of SWD and WD for multicomponent linear frequency-modulated (LFM) signals processing is then observed by exploring the factor k selection results on two kinds of bi-component cases, including the one with a different frequency rate and the other one with the same frequency rate but having a different initial frequency. Correctness of the derived results and the SWD’s superiority in the instantaneous frequency estimation of noisy LFM signals compared with the WD are illustrated through simulations, and finally further discussions point out some promising future research directions and perspectives.