Fast Algorithm for Fractional Fourier Transform

The Fractional Fourier Transform (FrFT) serves as a crucial mathematical tool in signal processing and image analysis. It operates as a transformation method that converts signals from the time domain to the frequency domain, similar to the traditional Fourier Transform (FFT). Compared to FFT, FrFT demonstrates superior capabilities in handling non-stationary signals and nonlinear systems. The fast algorithm for Fractional Fourier Transform implements an efficient computational approach based on convolution principles, achieving computational complexity comparable to standard FFT algorithms. This implementation typically involves decomposing the transform into a series of operations including chirp multiplication, standard FFT, and chirp convolution phases. Through the application of this fast FrFT algorithm, researchers and engineers can achieve more precise analysis and processing of complex signal patterns and image data structures, enabling advanced time-frequency analysis applications.