# Sinc Interpolation for Signal Reconstruction

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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.

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Contributed by: Nasser M. Abbasi (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The function is defined by for , with . The sinc interpolation formula is defined as , where is the sampling period used to determine from the original signal, and is the reconstructed signal. The above formula represents a linear convolution between the sequence and scaled and shifted samples of the function. In this Demonstration, a limited number of samples are generated, and the above sum is carried out for samples, labeled from to . Due to the shifting of the function by integer multiples of , this results in having the exact value of a sample located at a multiple of . This can be seen by observing that the absolute error is always zero at times which are integer multiples of , in other words at the sample locations. In this implementation, the function is sampled at a much higher rate than the sampling frequency used for the original function, in order to produce a smoother plotted result.

A. V. Oppenheim and R. W. Schafer, *Digital Signal Processing*, Englewood Cliffs, NJ: Prentice Hall, 1975.

## Permanent Citation

"Sinc Interpolation for Signal Reconstruction"

http://demonstrations.wolfram.com/SincInterpolationForSignalReconstruction/

Wolfram Demonstrations Project

Published: March 7 2011