where 
and 
are quantities defined by 
.
Further, the inverse real discrete Fourier transform is given by
,
( n = 0, 1, 2, …, N -1) (11.30)
We explain the characteristics of the spectra obtain by DFT using an example in the following. Figure 11.27(a) shows a square wave with period
T = 8 and sixteen sampled data: 
and 
obtained by sampling with interval 
. In this example, the signal is sampled intentionally in the range that coincides with the period of the original square wave to avoid the leakage error. Figure 11.27(b)-(e) shows spectra representing the real part of 
, the imaginary part of , the amplitude 
and the phase 
.