The Arithmetic Fourier Transform
Joel L. Schiff
TL;DR
The paper introduces the Arithmetic Fourier Transform, a fast, addition-only numerical method for computing Fourier and Taylor series coefficients, with potential advantages over FFT and connections to prime number theory.
Contribution
It presents the Arithmetic Fourier Transform as an efficient alternative to FFT, emphasizing its simplicity and parallelizability, and explores its theoretical links to prime number theorems.
Findings
AFT requires only addition operations.
AFT can be parallelized effectively.
AFT has competitive speed with FFT.
Abstract
The Arithmetic Fourier Transform is a numerical formulation for computing Fourier series and Taylor series coefficients. It competes with the Fast Fourier Transform in terms of speed and efficiency, requiring only addition operations and can be performed by parallel processing. The AFT has some deep connections with the Prime Number Theorem and its rich history is discussed in this expository article.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematical functions and polynomials · Analytic and geometric function theory