DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

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increases gradually to about 4 dB above its response at
DC, to compensate the loss. Above the passband edge
frequency, the response of the filter must decrease
rapidly to produce a large attenuation near half the
sampling frequency, to provide alias-free reconstruction.
The bottom graph of Figure 16.30 shows the idealized
response of a filter having (sin x)/x correction.
This chapter has detailed one-dimensional filtering. In
Image digitization and reconstruction, I will introduce
two- and three-dimensional sampling and filters.
Further reading
For an approachable introduction to the concepts,
theory, and mathematics of digital signal processing
(DSP), see Lyons. For an alternative point of view, see
Rorabaugh’s book; it includes the source code for
programs to design filters – that is, to evaluate filter
coefficients. For comprehensive and theoretical
coverage of DSP, see Mitra and Kaiser.
170 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES
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Frequency, multiple of f s
Figure 16.30 (sin x)/x correction is necessary following (or in principle, preceding) digital-toanalog
conversion when a DAC with a typical boxcar output waveform is used. The frequency
response of a boxcar-waveform DAC is shown in the upper graph. The lower graph shows the
response of the (sin x)/x correction filter necessary to compensate its high frequency falloff.
Lyons, Richard G., Understanding
Digital Signal Processing (Reading,
Mass.: Addison Wesley, 1997).
Rorabaugh, C. Britton, DSP Primer
(New York: McGraw-Hill, 1999).
Mitra, Sanjit K., and James F. Kaiser,
Handbook for Digital Signal
Processing (New York: Wiley, 1993).
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