TL;DR
This paper offers a novel interpretation of the continuous Fourier transform using the Chinese Remainder Theorem and discusses related topics like a new derivation of the Poisson summation formula.
Contribution
It introduces a new perspective on Fourier transform interpretation through number theory and provides a fresh derivation of the Poisson summation formula.
Findings
New interpretation of Fourier transform via Chinese Remainder Theorem
Derivation of Poisson summation formula from this perspective
Discussion of related mathematical issues
Abstract
In this note, we describe an interpretation of the (continuous) Fourier transform from the perspective of the Chinese Remainder Theorem. Some related issues, including a new derivation of Poisson summation formula, are discussed.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Numerical Analysis Techniques · Algebraic and Geometric Analysis