1991/09/01 by David A. Bailey, Paul N. Swarztrauber · 1 citation
Computer Science · Mathematics · #Digital Filter Design and Implementation #Mathematical Analysis and Transform Methods #Image and Signal Denoising Methods #Fractional Fourier transform #Discrete Fourier transform (general) #Mathematics #Non-uniform discrete Fourier transform #Discrete-time Fourier transform #Fourier transform #Algorithm #Prime-factor FFT algorithm #Discrete sine transform #Cyclotomic fast Fourier transform #Fast Fourier transform #Harmonic wavelet transform #Short-time Fourier transform #Fourier analysis #Mathematical analysis #Computer science #Wavelet transform #Discrete wavelet transform #Artificial intelligence #Wavelet
paper · doi:10.1137/1033097
openalex publication_date 1991/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
This paper describes the “fractional Fourier transform,” which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e^ - 2π i / n , the fractional Fourier transform is based on fractional roots of unity e - 2π iα where α is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.