When an analog signal x(t) is changed into a sequence of digital data 
( n = 0, 1, 2, …, N ) a virtual (or imaginary) wave is obtained if a fast signal is sampled slowly. For example, when a signal illustrated by the full line is sampled as shown in Figure 11.21, a virtual signal wave illustrated by the dashed line appears, although it is not contained in the original signal.
This phenomenon is called aliasing. It is obvious that we must sample with a smaller sampling interval as the signal frequency increases. We can determine whether or not we have this aliasing by following the sampling theorem. It says: when a signal is composed of the components whose frequencies are all smaller than 
we must sample it with a frequencies higher than 
or the sake of not losing the original signal's information. The frequency is called Nyquist frequency. For example, if a sine wave with period T is sampled whenever 
, that is, with sampling interval 
, we have 
. Therefore, two samplings in a period are clearly insufficient. However, this theorem teaches us that digital data with more than two points during one period can express the original signal correctly.