Fourier transform and its applications

  • Authors:

  • Luiza Grigorescu;Gheorghe Oproescu;Ioana Diaconescu;Cristian Simionescu

  • Affiliations:

  • "Dunarea de Jos" University of Galati, Galati, Romania;"Dunarea de Jos" University of Galati, Galati, Romania;"Dunarea de Jos" University of Galati, Galati, Romania;"Dunarea de Jos" University of Galati, Galati, Romania

  • Venue:
  • ACC'11/MMACTEE'11 Proceedings of the 13th IASME/WSEAS international conference on Mathematical Methods and Computational Techniques in Electrical Engineering conference on Applied Computing
  • Year:
  • 2011

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Abstract

This paper analyses Fourier transform used for spectral analysis of periodical signals and emphasizes some of its properties. It is demonstrated that the spectrum is strongly depended of signal duration that is very important for very short signals which have a very rich spectrum, even for totally harmonic signals. Surprisingly is taken the conclusion that spectral function of harmonic signals with infinite duration is identically with Dirac function and more of this no matter of duration, it respects Heisenberg fourth uncertainty equation. In comparison with Fourier series, the spectrum which is emphasized by Fourier transform doesn't have maximum amplitudes for signals frequencies but only if the signal lasting a lot of time, in the other situations these maximum values are strongly de-phased while the signal time decreasing. That is why one can consider that Fourier series is useful especially for interpolation of nonharmonic periodical functions using harmonic functions and less for spectral analysis.