Two-Dimensional Fractional Fourier Transform: Algorithm and Applications

The Two-Dimensional Fractional Fourier Transform (2D-FrFT) is a mathematical tool that converts data from its original form into the 2D fractional Fourier domain. This transformation plays a significant role in signal processing and image processing applications, enabling better understanding and analysis of data. Implementation typically involves applying separable fractional Fourier transforms along each spatial dimension, often computed through discrete approximations using eigenvector decomposition of the DFT matrix or sampling-based methods. By employing the 2D-FrFT, we can explore additional dimensions and features within data, leading to more accurate and comprehensive information extraction. Key programming considerations include proper parameterization of fractional orders and efficient computation using matrix multiplication techniques. Therefore, learning and applying the 2D-FrFT is essential for in-depth research and practical problem-solving in multidimensional signal analysis.