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
discrete-time
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 discrete-time samples.
![\includegraphics[width=\twidth]{eps/SincSum}](http://www.dsprelated.com/josimages_new/mdft/img1765.png) |
Notice that each sinc function passes through zero at every sample
instant but the one it is centered on, where it passes through 1.
Next Section: The Sinc FunctionPrevious Section: Time-Bandwidth Products
are Unbounded Above
![$\displaystyle x = [\dots, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, \dots]
$](http://www.dsprelated.com/josimages_new/mdft/img1764.png){kind=small}
