The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. In mathematics, the discrete Fourier transform ( DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. Its similarities to the original transform, S(f), and its relative computational ease are often the motivation for computing a DFT sequence. The respective formulas are (a) the Fourier series integral and (b) the DFT summation. ![]() The spectral sequences at (a) upper right and (b) lower right are respectively computed from (a) one cycle of the periodic summation of s(t) and (b) one cycle of the periodic summation of the s(nT) sequence. Fig 2: Depiction of a Fourier transform (upper left) and its periodic summation (DTFT) in the lower left corner.
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