Mathematics of the Discrete Fourier Transform (DFT)
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Decimation Operator
Definition: Decimation byis defined as taking every
:
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
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