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.