Fourier Series and Transforms via Convolution
Francisco Mota
TL;DR
This paper presents a novel approach to defining Fourier Series and Transforms through convolution with exponential signals, simplifying proofs and offering educational benefits.
Contribution
It introduces an alternative convolution-based method for Fourier analysis, enhancing understanding and proof simplicity.
Findings
Simplifies proofs of Fourier properties
Provides an educational perspective on Fourier analysis
Offers a new convolution-based definition
Abstract
In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view, may be interesting for educational purposes.
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Taxonomy
TopicsNumerical Methods and Algorithms