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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 is presented. The 2-D DTFT is also briefly presented.

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The Discrete-Time Fourier Transform

  • 章节

  • 发表日期：

    2025年

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  • D. Sundararajan

摘要

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 is presented. The 2-D DTFT is also briefly presented.