A convolution-based fractional transform

The fractional transforms are a class of powerful tool for the presentation of time-frequency domains in the field of signal processing. Based on the convolution algorithm of discrete fractional Fourier transform and gyrator transform, we propose a generalized framework defining a class of fractional transforms. By choosing various phase filters, the fractional transform can be employed for different computational tasks of information processing. The several properties of typical fractional transform are reserved in this definition scheme. Under the model of the convolution-based transform, fractional Fourier transform and gyrator transform are synthesized. Moreover, the transform can be implemented by an optical 4f system with phase-only filtering easily, which is a useful tool in the application of optical information processing. Numerical results are given for demonstrating the proposed transform and its application.