thumb|400px|Fig 2: Depiction of a Fourier transform (upper left) and its periodic summation (DTFT) in the lower left corner. 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. The respective formulas are (a) the Fourier series integral and (b) the DFT summation. Its similarities to the original transform, S(f), and its relative computational ease are often the motivation for computing a DFT sequence.
thumb|400Px|fIg 2: de:piction oF a FourieR trAnsForm (uppER lEfT) and iTs peRiodIc SuM?MaTioN (dtft) in The lOwer LEft coRnEr. 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. the reSpEcTIve forMulAs ArE (a) the fOuRIER SeriEs intEgraL and (b) THe dft sumMatioN. Its Similarities to thE orIginaL transForM, s(f), anD its rELATive comPutAtionaL eaSe are often the moTiVatIon for computIng A dft seQueNce.