Fourier Sum Definitions

            Time extends from T/2 to T/2 in N steps of Δ_t = T/N.  Frequency extends from  N/(2Δ_t) to N/(2Δ_t) in steps of Δ_f = 1/ NΔ_t = 1/Time. 

The DFT is fundamental, the integral relationships are induced.  The square brackets refer to discrete functions, defined only for integral values as in the book Discrete-time Signal Processing[1]

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