Decimation

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Definition Decrease sampling rate, too much can lead to Aliasing - Folding

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Use case Decimation filters help you remove the excess bandwidth and reduce the sampling frequency of the signal.

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Example: Decimation by a factor $D$ means: If $D=2$ and $x[n]=[1,2,3,4,5,4,3,2,1]$, then the down-sampled output will be:

$$\begin{array}{rl}y[m]& =x[n]{|}_{n=mD}=x[mD]\\ y[m]& =[1,3,5,3,1]\end{array}$$

The Rate of $x$ is $F_x=\frac{1}{T_x}$ and the Rate of y will be $F_y=\frac{F_x}{D}=\frac{1}{D{T}_x}$.

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Visually, decimation leads to “growing” in the frequency plane.