The Discrete-Time Fourier Transform

  • D. SundararajanEmail author


The DTFT version of the Fourier analysis is presented. The DTFT primarily represents aperiodic discrete signals by a continuous periodic spectrum. The DTFT definition is derived starting from the DFT definition. Examples of determining the DTFT of signals are given. The DTFT of a discrete periodic signal and the relation between the DFT and the DTFT spectra are established. The properties of the DTFT are derived and examples are given. Typical applications of the DTFT are presented. The numerical approximation of the DTFT by the DFT concludes the chapter.


DTFT Discrete-time Fourier transform Periodic Aperiodic Aliasing Time-limited Band-limited Differentiator Hilbert transform Impulse response Transfer function Frequency response 

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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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