Two-Dimensional Discrete Fractional Fourier Transform

This implementation of the two-dimensional discrete fractional Fourier transform program can be widely applied in digital image processing domains. The algorithm employs efficient matrix decomposition methods and fractional power calculations of eigenvalues to handle various image processing tasks including but not limited to noise reduction, edge detection, and image enhancement. The code structure utilizes separable transformation approaches where the 2D transform is computed as successive 1D fractional Fourier transforms along rows and columns, ensuring computational efficiency while maintaining mathematical precision. With excellent scalability and flexibility in its object-oriented design, the program supports parameter customization for different fractional orders and can be adapted to diverse application scenarios. The implementation includes optimized memory management for large image datasets and parallel processing capabilities for performance-critical applications. Therefore, whether in academic research or industrial practice, this two-dimensional discrete fractional Fourier transform program serves as an indispensable tool for advanced signal and image analysis.