傅里叶变换的单指数逼近
Single Exponential Approximation of Fourier Transforms
AI总结：
本文提出一种基于梯形法则的单指数收敛新求积规则，用于近似计算傅里叶正弦和余弦变换，并通过围道积分和鞍点法进行误差分析。
摘要：
本文研究一种近似计算傅里叶正弦和余弦变换的新方法。我们开发并分析了一种新的求积规则，该规则通过将积分变换到整个实轴上的积分，然后使用梯形法则来近似变换后的积分。该方法继承自Ooura和Mori的工作。利用围道积分进行了完整的误差分析。详细考察了一个例子，并使用留数和鞍点法分析了误差。我们开发的方法以其简单性和单指数收敛性为特征。
英文摘要：
This article is concerned with a new method for the approximate evaluation of Fourier sine and cosine transforms. We develop and analyse a new quadrature rule for Fourier sine and cosine transforms involving transforming the integral to one over the entire real line and then using the trapezoidal rule in order to approximate the transformed integral. This method follows on from the work of Ooura and Mori. A complete error analysis is made using contour integration. An example is examined in detail and the error is analysed using residues and the saddle point method. The method we have developed is characterised by its simplicity and single exponential convergence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
