Properties, digital implementation, applications, and self image phenomena of the gyrator transform

The gyrator transform was introduced in recent years and useful for image processing. As the fractional Fourier transform, the gyrator transform can also be viewed as an extension of the Fourier analysis. In this paper, we discuss the digital implementation algorithms of the gyrator transform. We also discuss the eigenfunctions and the self-imaging phenomena of the gyrator transform. Many properties, such as the differential and dilation preservation properties, are also discussed. We also discuss the possible applications of the gyrator transform in filter design and signal sampling.