Through the optimization of the main interval of the fractional order, an improved fast algorithm for numerical calculation of the fractional Fourier transforms is proposed. With this improved algorithm, the fractional Fourier transforms of a rectangular function and a Gaussian function are calculated. Its calculation errors are compared with those calculated with the previously published algorithm, and the results show that the calculation accuracy of the improved algorithm is much higher.
© 2004 Optical Society of America
Original Manuscript: November 20, 2003
Revised Manuscript: March 15, 2004
Manuscript Accepted: March 15, 2004
Published: September 1, 2004
Xingpeng Yang, Qiaofeng Tan, Xiaofeng Wei, Yong Xiang, Yingbai Yan, and Guofan Jin, "Improved fast fractional-Fourier-transform algorithm," J. Opt. Soc. Am. A 21, 1677-1681 (2004)