A novel rotated radial-shift compound operator

In this paper, we proposed the novel rotated radial-shift operator which first rotates a signal by an arbitrary angle in the time-frequency plane based on the fractional Fourier transform and then radially shifts the rotated signal along the rotation direction. We also proved that this operator is a generalized expression of many well-known operators such as the time-shift, the frequency-shift and the time-frequency-shift. After presenting the covariance property on the WVD that results from applying the operator to Gaussian function, we put forward the three-parameter chirp atom with the scale, the rotation and the radial-shift.