New Wigner Distribution and Ambiguity Function for the Offset Fractional Fourier Transform and Their Applications

This paper introduces the new offset fractional Fourier Wigner distribution and offset fractional Fourier ambiguity function (OFrWD and OFrAF). Moreover, many various useful properties of them are also derived. Besides, convolutions via offset fractional Fourier transform are also introduced. Furthermore, the relationships between proposed convolutions and the OFrWD as well as OFrAF are also obtained. In addition, with the help of simulation, applications of OFrWD and OFrAF are established, such as designing multiplicative filters in the offset fractional Fourier transform (OFrFT) domain and detecting the parameters of single-component and multicomponent linear frequency-modulated (LFM) signals.