A novel symmetry property of the Fourier transform
DOI:
https://doi.org/10.31349/RevMexFis.71.061303Keywords:
Fourier transform; signal processing; parseval theoremAbstract
This manuscript presents and proves a reciprocity relation involving the Fourier transforms of a pair of square-integrable functions, expressed as a bilinear map. This reciprocity relation reveals a deep symmetry between the time (or spatial) and frequency domains. We explore its implications in theoretical and applied contexts such as signal processing, quantum mechanics, and computational physics. Additionally, we discuss the role of this relation in the bilinear nature of Fourier analysis.
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