Definition: Decimation by is defined as taking every th sample, starting with sample :
The operator maps a length signal down to a length signal. It is the inverse of the operator (but not vice versa), i.e.,
The stretch and decimation operations do not commute because they are linear time-varying operators. They can be modeled using time-varying switches controlled by the sample index .
Figure:Illustration of . The white-filled circles indicate the retained samples while the black-filled circles indicate the discarded samples.
An example of is shown in Fig. 8.8. The example is