Two-Dimensional Discrete Coupled Fractional Fourier Transform (DCFrFT)

The fractional Fourier transform is critical in signal processing and supports many applications. Signal processing is one notable application. Implementing the fractional Fourier transform requires discrete versions. As a result, defining a discrete coupled fractional Fourier transform (DCFrFT) is essential. This paper presents a discrete version of the continuous, two-dimensional coupled fractional Fourier transform, which is not a tensor product of one-dimensional transforms. We examine the main characteristics of the operator and illustrate its relationship with the existing two-dimensional discrete fractional Fourier transforms. Examples help clarify the approach.