Fourier transforms are used for obtaining the frequency spectrum of a signal. For instance, in nuclear magnetic resonance spectroscopy, a molecule’s spin in a magnetic field is analyzed to discover its oscillation frequencies and draw conclusions about its chemical consistency. In this work, the basic definitions and elementary mathematical properties of the Fourier integral, used as the main theoretical tool in Fourier transform analysis, were studied, together with some applications of these properties in computing the Fourier integral of some functions perceived as time signals in order to discover their frequency spectra.
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