Algorithm for Performing Fractional Fourier Transform

In mathematics, the fractional Fourier transform (FRFT) is a linear transformation algorithm that generalizes the classical Fourier transform to fractional orders. This algorithm can transform functions of arbitrary fractional orders, offering greater flexibility and broader applications compared to traditional integer-order Fourier transforms. The implementation typically involves eigenvalue decomposition of the Fourier operator or discrete approximation methods using transformation kernels. Through fractional Fourier transform, we can perform more refined signal analysis and processing in areas such as signal denoising, image processing, and medical signal analysis. Key computational approaches include the discretization of the continuous FRFT using sampling techniques and matrix multiplication methods. Therefore, understanding the principles and applications of fractional Fourier transform, along with its algorithmic implementation using numerical computation libraries, is essential for advanced signal processing applications.