Interpolation

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Definition Increase sampling rate, and “create” data between points.

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Use case Interpolation filters help you avoid Aliasing - Folding.

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Example Decimation by a factor $I$ means: The interpolated output will be (we also use an intermediate variable, $v$, look at the slides):

$$\begin{array}{rl}y[m]& =x[n]{|}_{n=\frac{m}{I}}=x\left[\frac{m}{I}\right]\end{array}$$

The Rate of $x$ is $F_x=\frac{1}{T_x}$ and the Rate of $v$ will be $F_v=I{F}_x$

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Visually, interpolation leads to “shrinking” in the frequency plane.