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.
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