Discrete fractional Fourier transform algorithm via fractional domain decomposition

An algorithm of discrete fractional Fourier transform (DFRFT) using fractional domain decomposition is proposed. With this method, the DFRFT of a signal at any fractional domain can be obtained by a weighted linear summation of its DFRFTs at certain special fractional domains. The weighting coefficients are calculated by an IDFT computation of a series consisted of DFT Hermite eigenvalues with appended zeros. Theoretic analysis and numerical simulation results indicate that this method not only derives similar results as the comentional eigenvector based DFRFT method. but also reduces computational burdens efficiently in searching optimal fractional domain. It can be used for multi-component signal detection and filtering in fractional Fourier domains.