Novel fractional scaled Wigner distribution using fractional instantaneous autocorrelation

The traditional scaled Wigner distribution (SWD) is extended to a novel one inspired by merits of fractional instantaneous autocorrelation present in the definition of fractional bi-spectrum and the fractional Fourier transform (FrFT). We begin by examining the basic characteristics of the novel fractional scaled Wigner distribution (Fr-SWD), such as its nonlinearity, marginality, shifting, conjugate symmetry, and antiderivative nature. Following that, a thorough analysis of Moyal’s formula is also conducted. The proposed distribution is used to detect both single-component and multi-component linear frequency-modulated signals in order to demonstrate its effectiveness. The results of the simulation clearly show that the novel fractional scaled Wigner distribution performs exceptionally well in comparison with the conventional Wigner distribution and its scaled version.