一种改良的啁啾变换算法及其应用

快速啁啾算法引入两次快速傅里叶变换（FFT）及一个解析高斯核，计算复杂度低于卷积算法.通过对啁啾算法实现过程进行的改进，避免了该算法在实现过程中存在的一些问题，比如输出窗口小、信号丢失、计算复杂度稍大等缺点. 把算法用于简单的可求得解析解的系统并与之做比较. 对高斯函数，最大误差通常在10^-15数量级，而对矩形函数，由于受FFT算法计算精度的影响，误差在10^-3数量级，但这并不影响算法的性能. 最后把算法用于一种典型的标量衍射系统及分数傅里叶变换的计算,获得了很好的结果. 关键词： 快速啁啾算法 啁啾Z变换 菲涅耳变换 分数傅里叶变换

An improved fast algorithm for chirp transforms and its applications

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.