Delta function of the Fourier transform

Abstract

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.

Keywords

• delta function
• fourier transform
• window transform
• double fourier