A new fractional wave packet transform

Abstract The fractional Fourier transform (FRFT) has been shown to be powerful tool for optics and signal processing. However, it fails in locating the fractional domain frequency contents which is required in some applications. In this paper, a new fractional wave packet transform (FrWPT) is proposed to address this problem, based on the wave packet transform (WPT) and FRFT. It preserves the properties of classical WPT and has better mathematical properties. First, we derived some fundamental results of the FrWPT, including its basic properties, inversion formula and admissibility condition and the reproducing kernel. Further, the relationship between the FrWPT and Wigner distribution is presented. Lastly, we show that the energetic form of the FrWPT the fractional wavepacketgram, i.e., the modulus square of the FrWPT is a member of the Cohen class time-frequency distribution where the kernel is a scale dependent ambiguity function.