Title :
On the Angular Decomposition Technique for Computing the Discrete Fractional Fourier Transform
Author :
Hanna, Magdy Tawfik
Author_Institution :
Dept. of Eng. Math. & Phys., Fayoum Univ.
Abstract :
The angular decomposition technique for computing the discrete fractional Fourier transform (DFRFT) at an arbitrary angle as a weighted sum of the DFRFTs at a set of equispaced angles is refined by presenting a unified mathematical framework encompassing both cases of even and odd length sequences. A mathematically sound simple closed-form expression for the coefficients of the weighted sum is derived. The special case of real sequences is treated in more detail showing that the computational load of finding the DFRFTs at the set of predefined equispaced angles can be almost halved.
Keywords :
discrete Fourier transforms; eigenvalues and eigenfunctions; Hermite-Gaussian-like eigenvectors; angular decomposition technique; computational load; discrete fractional Fourier transform; eigendecomposition; Discrete Fourier transforms; Discrete transforms; Fourier transforms; Kernel; Mathematics; Matrix decomposition; Physics computing; Time domain analysis; DFT matrix; Discrete fractional Fourier transform; Hermite-Gaussian-like eigenvectors; eigendecomposition;
Conference_Titel :
Circuits and Systems, 2007. ISCAS 2007. IEEE International Symposium on
Conference_Location :
New Orleans, LA
Print_ISBN :
1-4244-0920-9
Electronic_ISBN :
1-4244-0921-7
DOI :
10.1109/ISCAS.2007.378674
