A time-variant filtering approach for non-stationary random signals based on the fractional convolution

• The properties of α-Wigner-Ville (α-WVD) distribution are studied.
• The association between fractional power spectral density and α-WVD is established.
• It is proved that fractional convolution (FrC) is a time-variant (TV) operation.
• Based on FrC was proposed a method for TV filtering for non-stationary signals.
• The methodology for more general signals, whose WVD have curved supports, is adapted.

This paper presents a time-variant filtering based on a notion of fractional convolution and its relation with α-Wigner–Ville distribution. Additionally, some properties of the α-Wigner–Ville distribution are studied. These properties also demonstrate that conventional theory based on Fourier Analysis is a particular case of the theory proposed in this paper. Finally, the paper wraps up showing that this development may lead to an adaptive filtering technique, thus extending their range of application.