- One period of a discrete-time sinusoidal signal of integer period length
*N*samples is given by

(1) - Figure 1 illustrates such a sinusoidal signal for
*N*= 32. - Clearly, the sum of the signal values of
*w*[*n*] is zero:

(2) - This result can be generalized to any sinusoidal signal of non-zero frequency when summed over an integral number of periods.
- Figure 2 illustrates the result of performing a point-wise multiplication of
*w*[*n*] with itself (essentially squaring each signal value). Note that the signal period is halved (the frequency is doubled) and that all the values are . - The sum of the signal values of
*w*^{2}[*n*] will be greater than zero (which indicates a DC offset). The sum of these values is equal to*N*/2, where*N*is the length of the period in samples.

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