An improved fast algorithm for chirp transforms and its applications

Abstract

A fast algorithm for chirp Z-transforms is improved form chirp Z-transform, which is developed by using two fast Fourier transforms and an analytical Gaussian kernel. Its computational complexity is less than a fast convolution algorithm. However, there are some problems when the algorithm is implemented, such as the discarding of the data, the smallness of the response domain, the bigness of the computational complexity and so on. To avoid the problems mentioned above, we make a change on the implementing of the algorithm in this paper. Then we compare the numerical results of some chirp systems with the analytical ones. The accuracy of Fourier transforms of Gaussian function is higher than the 10-15 order for most cases, and the accuracy of Fourier transforms of rectangle function is about the 10-3 order, which is essentially limited by the accuracy of the fast Fourier transform. Finially this algorithm is used to calculate some typical systems of scalar diffraction and fractional-order Fourier transforms, and the results are in good agreement with other published results in the literatures.