HSP50110
The Integrate and Dump filter exhibits a frequency response
examples of compensation filter performance for the Integrate
and dump and third order CIC filter are shown overlaid on the
frequency responses of the uncompensated filters in Figure 6
and Figure 7. The coefficients for the compensation filters are
given in Table 2.
given by
I
---
H(f) = sin(πfR)/sin(πf)
(EQ. 8)
R
where f is normalized frequency relative to the input sample
10
rate, F , and R is the decimation rate [1]. The decimation
S
rate is equivalent to the number of samples in the integration
period. As an example, the frequency response for an
integrate and dump filter with decimation of 64 is shown in
Figure 6. The decimation rate is controlled by the
Re-Sampler and may range in value from 2 to 4096 (see
Re-Sampler Section).
0
COMPENSATION
FILTER
COMPOSITE FILTER
-10
-20
-30
-40
-50
-60
CIC
FILTER
10
COMPOSITE FILTER
0
COMPENSATION
FILTER
-10
CIC
FILTER
-20
-30
-40
-50
-60
f
f
3f
2f
5f
3f
7f
4f
S
S
S
S
S
S
S
S
2R
R
2R
R
2R
R
2R
R
SAMPLE TIMES
NOTE: Example plotted is for R = 64 with 64 samples/symbol.
FIGURE 7. THIRD ORDER CIC FREQUENCY RESPONSE
TABLE 2. COMPENSATION FILTER COEFFICIENTS
3
f
f
3f
2f
5f
3f
7f
4f
S
S
S
S
S
S
S
S
COEFFICIENT INDEX
x/sin(x) [2]
[x/sin(x)]
-1
2R
R
2R
R
2R
R
2R
R
0
1
-1
2
SAMPLE TIMES
NOTE: Example plotted is for R = 64 with 64 samples/symbol.
4
FIGURE 6. INTEGRATE AND DUMP FILTER (FIRST ORDER
CIC) FREQUENCY RESPONSE
2
-4
-16
32
3
10
-34
384
-34
10
-4
For applications requiring better out of band attenuation, the
Third Order CIC filter may be selected. This filter has a
frequency response given by
4
-64
136
-352
1312
-352
136
-64
32
5
3
3
6
H(f) = [sin(πfR)/sin(πf)] [1/R]
(EQ. 9)
7
where f is normalized frequency relative to the input sample
rate, and R is the decimation rate [1]. As with the integrate
and dump filter, the decimation rate is controlled by the Re-
Sampler. The decimation rate may range in value from
2-4096 when using CLK, or 3-4096 when using the Re-
Sampler NCO as a CLK source to the filter. The frequency
response for the third order CIC with a decimation rate of 64
is shown in Figure 7.
8
9
2
10
11
12
13
14
-1
-16
4
Compensation filters may be activated to flatten the frequency
responses of the integrate and dump and third order CIC
filters. The compensation filters operate at the decimated data
rate, and flatten the roll off the decimating filters from DC to
approximately one half of the output sample rate. Together,
the Integrate and Dump filter and x/sin(x) compensation filter
typically yield a lowpass frequency response that is flat to
-1
The out of band channels and noise attenuated by the
decimating filters are aliased into the output spectrum as a
result of the decimating process. A summation of the alias
terms at each frequency of the output spectrum produce
alias profiles which can be used to determine the usable
output bandwidth. A set of profiles representative of what
would be observed for decimation factors of ~10 or more are
shown in Figures 8 through 11. The Integrate and Dump
filter is typically used as a matched filter for square pulses
0.45F with 0.03dB of ripple, and the third order CIC with
S
3
((x)/sin(x)) compensation typically yields a flat passband to
0.45F with 0.08dB of ripple. The overall passband ripple
S
degrades slightly for decimation rates of less than 10. Some
3-236
INTERSIL [ Intersil ]
