A Novel Rotated Radial-Shift Compound Operator

摘要

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 shifts -radially 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 resulted from applying the operator to Gaussian function, we put forward the three-parameter Chirp atom with the scale, the rotation and the radial-shift.