Figure
D.1 shows how a sound is reconstructed from its
samples. Each sample can be considered as specifying the
scaling and
location of a
sinc function. The
discretetime
signal being interpolated in the figure is
a
digital rectangular pulse:
The
sinc functions are drawn with dashed lines, and they sum to
produce the solid curve. An isolated sinc function is shown in
Fig.
D.2. Note the ``Gibb's overshoot'' near the corners of the
continuous rectangular pulse in
Fig.
D.1 due to bandlimiting. (A true continuous rectangular
pulse has infinite
bandwidth.)
Figure D.1:
Summation of weighted sinc
functions to create a continuous waveform from discretetime samples.

Notice that each sinc function passes through zero at every sample
instant but the one it is centered on, where it passes through 1.
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are Unbounded Above