# sinc interpolator

Perfect interpolator to recover a continuous signal \(x_r(t)\) from sampled sequence \(x[n]\) when the criterion in the shannon-nyquist theorem is fulfilled.

\begin{equation}
x_r(t) = \sum_{n=-\infty}^{\infty}x[n] sinc(\frac{\pi(t-nT)}{T})
\end{equation}

where \(sinc\) is the sinc function, \(T\) is the sampling period.

This is nonrealizable because the sinc function is infinite in the
time domain, **and** you need an infinite number of sinc functions.

The idea of resampling refers to manipulating the sampling rate.