The Fourier Transform

  • D. SundararajanEmail author


The FT version of the Fourier analysis is presented. FT is the most general version of the Fourier analysis and it is capable of representing all types of signals. However, it is mostly used to represent continuous aperiodic signals by continuous aperiodic spectra. The FT is derived starting from the FS definition. Examples of finding the FT of signals are given. Properties of the FT are presented next with examples. Then, the representation of all types of signals by the FT is described. The aliasing effect is presented from the frequency-domain point of view. Typical applications of the FT are given. The numerical approximation of the FT by the DFT concludes the chapter.


Fourier transform Spectrum Mixed class of signals Aliasing Truncation Signal energy 

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Formerly at Department of Electrical and Computer EngineeringConcordia UniversityMontrealCanada

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