International Conference «Mathematical and Information Technologies, MIT-2016»

28 August – 5 September 2016

Vrnjacka Banja, Serbia – Budva, Montenegro

Babić R.V.  

Infinity and infinitesimal in interpretation of Fourier Transform nature

The Fourier Transform (FT) is a proven powerfull tools in signal analysis. Using the concepts of infinity and infinitesimal we attempt to relate real world of signals with mathematical world of their representations thereby revealing some aspects of the nature of FT. Firstly, we give interpretation of time domain infinity through formalisation of a signal by respective mathematical function. Then we discuss another case of infinity and infinitesimal given in interrelation between Fourier series and FT. Particular attention we paid to the spectral characteristic of aperiodic function as a mathematical entity which prominently shows how these two concepts stems one from another. The issue of signal i.e. function reconstruction from its spectrum serves to consider infinity from another side where we discuss effects of simple trigonometric functions with infinitesimal frequences. Further we examine relation between the spectral peak and its limit represented by Dirac's function in order to interpret the notion of spectral line.

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