DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 16.17 5-tap
FIR filter responses
are shown for several
choices of coefficient
values (tap weights).
Magnitude response, dB
Figure 16.18 5-tap FIR
filter including multipliers
has coefficients [13, 56,
118, 56, 13], scaled by 1 ⁄ 256 .
The coefficients approximate
a Gaussian; so does the
frequency response. The
multipliers can be implemented
by table lookup.
0
-10
-20
-30
-40
0
{-32, 72, 176, 72, -32}
{13, 56, 118, 56, 13}
{1, 1, 1, 1, 1}
0.2π 0.4π 0.6π 0.8π π
Frequency, ω, rad·s -1
In the design of digital filters, control of frequency
response is exercised in the choice of tap weights.
Figure 16.18 below shows the block diagram of a filter
having fractional coefficients chosen from a Gaussian
waveform. The mid-gray curve in Figure 16.17 shows
that this set of tap weights yields a lowpass filter having
a Gaussian frequency response. By using negative coefficients,
low-frequency response can be extended
without deteriorating performance at high frequencies.
The black curve in Figure 16.17 shows the response of
a filter having coefficients [ -32⁄ 256, 72⁄ 256, 176⁄ 256,
72⁄ 256 , -32⁄ 256 ]. This filter exhibits the same attenuation
at high frequencies (about -18 dB) as the Gaussian, but
has about twice the -6 dB frequency.
Negative coefficients, as in the last example here,
potentially cause production of output samples that
exceed unity. (In this example, output samples above
unity are produced at input frequencies about ω=0.3π,
IN R R R R
13 56
256 256
118 56 13
256 256 256
CHAPTER 16 FILTERING AND SAMPLING 155
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