DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 16.12 [1, 1] FIR
filter sums two adjacent
samples; this forms a simple
lowpass filter. I’ll introduce
the term FIR on page 157.
Figure 16.13 [1, -1] FIR
filter subtracts one sample
from the previous sample;
this forms a simple highpass
filter.
Figure 16.14 [1, 0, 1] FIR
filter averages a sample and
the second preceding
sample, ignoring the sample
in between; this forms
a bandreject (“notch,” or
“trap”) filter at 0.25 f S .
Figure 16.15 [1, 0, -1] FIR
filter subtracts one sample
from the second previous
sample, ignoring the sample
in between; this forms
a bandpass filter centered at
0.25 f S .
2
1
0
0
2
1
2
1
Frequency, ω, rad·s (=1·fS )
-1
π 2π
0
0 π
Frequency, ω, rad·s
2π
-1
2
1
0
0 π
Frequency, ω, rad·s
2π
-1
0
0 π
Frequency, ω, rad·s
2π
-1
Digital filters can be implemented in software, firmware,
or hardware. At the right side of each graph
above, I show the block diagrams familiar to hardware
designers. Each block labelled R designates a register;
a series of these elements forms a shift register.
A simple highpass filter (HPF) is formed by subtracting
each sample from the previous sample: This filter has
weights [1, -1]. The response of this filter is graphed in
Figure 16.13. In general, and in this case, a highpass
CHAPTER 16 FILTERING AND SAMPLING 153
IN
IN
IN
R
IN R
R
R
R
R
+1
+ 1
1
+1
+1
+ 1
1
+1
OUT
OUT
OUT
OUT