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The Fourier series version of the Fourier analysis is presented. The FS represents continuous periodic signals by an aperiodic discrete spectrum. The FS representation is derived starting from that of the DFT. Several examples of finding the FS of signals are given, and the Gibbs phenomenon in the convergence of signals at discontinuities is explained. The properties of FS are presented along with examples. Typical applications of the FS in analyzing periodic signals are given. The numerical approximation of the FS and its inverse by the DFT are presented. The 2-D FS is also briefly presented.

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Fourier Series

  • 章节

  • 发表日期：

    2025年

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  • D. Sundararajan

摘要

The Fourier series version of the Fourier analysis is presented. The FS represents continuous periodic signals by an aperiodic discrete spectrum. The FS representation is derived starting from that of the DFT. Several examples of finding the FS of signals are given, and the Gibbs phenomenon in the convergence of signals at discontinuities is explained. The properties of FS are presented along with examples. Typical applications of the FS in analyzing periodic signals are given. The numerical approximation of the FS and its inverse by the DFT are presented. The 2-D FS is also briefly presented.