Fractional Fourier transform (FRFT) is a generalization of the Fourier transform, rediscovered
many times over the past 100 years. In this paper, we provide an overview of recent …

The fractional Fourier transform is a generalization of the classical Fourier transform, which
is introduced from the mathematic aspect by Namias at first and has many applications in …

Shift and rotation invariance properties of linear time-frequency representations are
investigated. It is shown that among all linear time-frequency representations, only the short …

A new signal-adaptive joint time–frequency distribution for the analysis of nonstationary
signals is proposed. It is based on a fractional-Fourier-domain realization of the weighted …

This correspondence investigates the uncertainty principles under the linear canonical
transform (LCT). First, a lower bound on the uncertainty product of signal representations in …

We review the progress achieved in optical information processing during the last decade by
applying fractional linear integral transforms. The fractional Fourier transform and its …

This paper proposes a time–frequency (t–f) image enhancement method for suppressing
interference terms in the Wigner–Ville distribution. The proposed technique adapts the …

The paper presents a systematic and unified approach to fractional integral transforms. We
introduce a new class of fractional integral transforms that includes the fractional Fourier and …

Based on the definition of the instantaneous frequency (signal phase derivative) as a local
moment of the Wigner distribution, we derive the relationship between the instantaneous …

The Fractional Fourier transform (FRFT) is a relatively novel linear transforms that is a
generalization of conventional Fourier transform (FT). FRFT can transform a particular signal …