Fourier Theorems for the DFT

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). Fourier Theorems for the DFT

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Fourier Theorems for the DFT

This chapter derives various Fourier theorems for the case of the DFT. Included are symmetry relations, the shift theorem, convolution theorem,correlation theorem, power theorem, and theorems pertaining to interpolation and downsampling. Applications related to certain theorems are outlined, including linear time-invariant filtering, sampling rate conversion, andstatistical signal processing.



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