| Issue |
E3S Web Conf.
Volume 535, 2024
XIII International Scientific and Practical Forum “Environmental Aspects of Sustainability of Construction and Management of Urban Real Estate” (ESCM-2024)
|
|
|---|---|---|
| Article Number | 01006 | |
| Number of page(s) | 5 | |
| Section | Innovative and Technical Solutions to Ensure Environmental Sustainability in Construction | |
| DOI | https://doi.org/10.1051/e3sconf/202453501006 | |
| Published online | 11 June 2024 | |
Delta function of the Fourier transform
1 All-Russian Research Institute of Optical and Physical Measurements (VNIIOFI), 46, Ozernaya street, Moscow, Russia
2 Moscow State University of Civil Engineering, 26, Yaroslavskoye Shosse, Moscow, 129337, Russia
3 École de Technologie Supérieure (ÉTS), 1100 R. Notre Dame O, Montréal, QC H3C 1K3, Canada
1 Corresponding author: schubert.maignan@gmail.com
In the analysis of the double window Fourier transform, it is found that both components of the direct transformation contain an equal amount of information sufficient to restore the original time signal. A double conversion diagram has been constructed. For any initial signal, there is a conjugate signal having the same frequency spectrum. Analysis of the harmonic signal transformation showed that at an arbitrary phase of the harmonic, the frequency representation contains two functions: conditionally unipolar with a maximum at the initial frequency and bipolar with a zero value at the specified frequency. For classical Fourier transformations with an infinite limit of integration, these functions turn into two delta functions with the same properties. The practical application of the found patterns is currently limited by the lack of an algorithm that allows the use of data from only one component.
Key words: delta function / Fourier transform / Window transform / Double Fourier
© The Authors, published by EDP Sciences, 2024
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