Signal Processing - Special section: Advances in signal processing-assisted cross-layer designs
Time delay estimation using fractional Fourier transform
Signal Processing
Signal processing issues in diffraction and holographic 3DTV
Image Communication
Discrete fractional Fourier transform based on orthogonalprojections
IEEE Transactions on Signal Processing
The discrete fractional Fourier transform
IEEE Transactions on Signal Processing
Digital computation of the fractional Fourier transform
IEEE Transactions on Signal Processing
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By using a spectral approach, we derive a Gaussian-like quadrature of the continuous fractional Fourier transform. The quadrature is obtained from a bilinear form of eigenvectors of the matrix associated to the recurrence equation of the Hermite polynomials. These eigenvectors are discrete approximations of the Hermite functions, which are eigenfunctions of the fractional Fourier transform operator. This new discrete transform is unitary and has a group structure. By using some asymptotic formulas, we rewrite the quadrature in terms of the fast Fourier transform (FFT), yielding a fast discretization of the fractional Fourier transform and its inverse in closed form. We extend the range of the fractional Fourier transform by considering arbitrary complex values inside the unit circle and not only at the boundary. We find that this fast quadrature evaluated at $z=i$ becomes a more accurate version of the FFT and can be used for nonperiodic functions.