# Sinc Interpolation for Signal Reconstruction

Sinc Interpolation for Signal Reconstruction

This Demonstration illustrates the use of the sinc interpolation formula to reconstruct a continuous signal from some of its samples. The formula provides exact reconstructions for signals that are bandlimited and whose samples were obtained using the required Nyquist sampling frequency, to eliminate aliasing in the reconstruction of the signal.

You can apply the interpolation formula to a number of continuous signals. Increasing the sampling frequency gives a more accurate reconstruction of the continuous function.

The original signal is shown as a blue solid line and the sample locations are shown by red circles. The reconstructed signal is shown using the dotted magenta line and is superimposed on the original signal to make it easier to see the effect of increasing the sampling frequency on the reconstruction of the original signal from its samples.

Because the number of samples is limited, there will be some error in the reconstruction, even at a higher sampling frequency than the Nyquist frequency. The absolute (point by point) error shown by the original signal and the reconstructed signal is plotted to show how the error decreases as the sampling rate increases.