The Arithmetic Fourier Transform

本研究解决了一种称为算术傅立叶变换（AFT）的算法的研究，用于精确的高速傅立叶分析和合成。AFT是基于莫比乌斯反演的数论方法。它的计算是并行进行的，除了在计算的一个阶段中进行少量的缩放外，它只使用乘以0、+1和-1。在研究这个变换的性质和量化这个变换与其他傅里叶分析方法相比的优势方面正在进行工作。

This research addresses the study of an algorithm called Arithmetic Fourier Transform (AFT) for accurate high-speed Fourier analysis and synthesis. The AFT is based on the number theoretic method of Mobius Inversion . Its computations proceed in parallel and except for a small number of scalings in one stage of the computation, uses only multiplications by 0, +1 and -1. Work is being carried out in studying the properties of this transform and quantifying the advantages of this transform in comparison to other approaches to Fourier analysis.