Expositio paper exp-20260820-872577
Infinite Series Through Fourier Analysis
In this paper, we will introduce Fourier Series through the Orthogonality Relations from which we consider Parseval's Theorem. Then, we wish to extend the concept of Fourier Series of aperiodic functions, specifically showing the Fourier Transform. The usage …
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Abstract
In this paper, we will introduce Fourier Series through the Orthogonality Relations from which we consider Parseval's Theorem. Then, we wish to extend the concept of Fourier Series of aperiodic functions, specifically showing the Fourier Transform. The usage of the Fourier Transform brings curious phenomena as shown by Shannon and Nyquist in their respective papers, which we mention in an example.
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