DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

1
1+
sin 0.44 ωt
2
0.5
Figure 16.28 Reconstruction
close to 0.5f S
0
1
0.5
0
2 3 4 5 6 7
Reconstruction close to 0.5f S
Consider the example in Figure 16.28 of a sine wave at
0.44f S. This signal meets the sampling criterion, and
can be perfectly represented in the digital domain.
However, from an intuitive point of view, it is difficult
to predict the underlying sinewave from samples 3, 4,
5, and 6 in the lower graph. When reconstructed using
a Gaussian filter, the high-frequency signal vanishes. To
be reconstructed accurately, a waveform with
a significant amount of power near half the sampling
rate must be reconstructed with a high-quality filter.
(sin x)/x correction
I have described how it is necessary for an analog
reconstruction filter to follow digital-to-analog conversion.
If the DAC produced an impulse “train” where the
amplitude of each impulse was modulated by the corresponding
code value, a classic lowpass filter would
suffice: All would be well if the DAC output resembled
my “point” graphs, with power at the sample instants
and no power in between. Recall that a waveform
comprising just unit impulses has uniform frequency
response across the entire spectrum.
Unfortunately for analog reconstruction, a typical DAC
does not produce an impulse waveform for each
sample. It would be impractical to have a DAC with an
168 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES