Decimation Operator

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). Decimation Operator

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Decimation Operator



Definition: Decimation by $L$is defined as taking every $L$th sample, starting with sample $0$:

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The $\ operator maps a length $N=LM$ signal down to a length $M$signal. It is the inverse of the $\ operator (but not vice versa), i.e.,

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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 $n$.

Figure:Illustration of $\. The white-filled circles indicate the retained samples while the black-filled circles indicate the discarded samples.
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An example of $\ is shown in Fig. 8.8. The example is

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