Periodic functions and the discrete Fourier transform: a time-domain view

The discrete Fourier transform (DFT) is often used to compute the Fourier series coefficients of periodic functions. Most explanations of this process rely on advanced concepts from Fourier transform theory; as an alternative, it is shown by the author that the DFT may be derived solely in the time domain, and that this derivation leads to the well-known relation between sampling rate and aliasing. Also included is an extension of the DFT to multiple dimensions.<
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