MATLAB Implementation of Discrete Fractional Fourier Transform Algorithm

This document presents a MATLAB implementation of the discrete fractional Fourier transform (DFrFT) algorithm. The program is designed for processing specialized signals and waveforms, where the fractional Fourier transform enables enhanced analysis of signal spectral characteristics in fractional domains. The MATLAB implementation features several key components: - Core transformation functions handling both forward and inverse fractional Fourier transforms - Parameterized fractional order control allowing continuous interpolation between time and frequency domains - Efficient matrix-based computation using eigen decomposition of DFT matrices The program accepts input signals and computes their fractional Fourier coefficients through discrete algorithm implementation. It supports both transformation and inverse transformation operations, maintaining numerical stability through orthogonal eigenvector bases. Key functions include: - frft_matrix(): Generates the transformation matrix for specified fractional orders - dfrft(): Main function performing the discrete fractional Fourier transform - idfrft(): Inverse transform function for signal reconstruction This implementation serves dual purposes: providing practical tools for signal processing applications while facilitating deeper understanding of fractional Fourier transform principles. The code structure allows researchers to explore fractional domain properties, analyze time-frequency distributions, and develop customized signal processing techniques. The program offers valuable utilities for both academic research and practical applications in fractional Fourier transform studies, particularly in areas such as signal filtering, chirp signal analysis, and time-frequency representation optimization.