IEEE Circuits and Systems Magazine - Q1 2018 - 21
resolution that would practically justify the need for
an 80-dB attenuation. An optimally-factored IFIR design of this filter is shown in Fig. 10(a), based on the
optimal factoring technique [46], [47], [57], [58] where
the factored cascade structure can easily be pipelined
[46]. Each stage in the optimally-factored cascade is
followed by a power-of-two scaling and a truncation
(or rounding) to efficiently manage the wordlength of
the data path [46]. The bound in (11), the solid line in Fig. 11
when min ^d p, d s h = 0.0001 , predicts that a practical
realization of this FIR filter requires a minimum of approximately 3860 flip-flops and full adders, using a = 1
in (11). The gray area in Fig. 11 again indicates the region that is predicted to be practically unreachable, or
quite unlikely to be realizable (especially for the denser gray areas) when the target has min ^d p, d s h = 0.0001.
1/2
1+z -12
-2
-0.125(z +z
-10
-4
-8
)+0.625(z +z )+2z
1/4
1+1.5z -1+z -2
-6
1
1/2
1+z
-12
-2
-2.59375(z +z
-10
-4
-8
)+1.25(z +z )+0.875z
-6
1+0.75z -2+z -4
1/2
1/2
1+1.75z -2+z -4
1+0.5z -2+z -4
1/2
1+z -14-0.96875(z -2+z -12)-0.15625(z -4+z -10)+1.21875(z -6+z -8)
1/2
1/4
1+1.875z -2+z -4
1+0.375z -2+z -4
1/2
-2
1+z -2
1+z -8-1.25(z -2+z -6)
1/4
-1/8
1-4(z
1+2z -1+z -2
-2+z -3)+z -5
(a)
Magnitude (dB)
0
-10
Magnitude (dB)
-20
-30
-40
0.2
0.1
0
-0.1
-0.2
-50
0
0.05
0.5
ω /π
0.6
-60
0.1
ω /π
0.15
0.2
-70
-80
-90
-100
0
0.1
0.2
0.3
0.4
0.7
0.8
0.9
1
Order-62 Wideband FIR Filter [56]
Optimally Factored Interpolated FIR Design
(b)
Figure 8. An optimally-factored implementation [46], [47], [57], [58] of the filter specification in Example 2 and the corresponding
magnitude plot. Each stage in the optimally-factored cascade is followed by a power-of-two scaling and a truncation (or rounding)
to efficiently manage the wordlength of the data path [46].
fIrst quArtEr 2018
IEEE cIrcuIts ANd systEMs MAgAzINE
21
Table of Contents for the Digital Edition of IEEE Circuits and Systems Magazine - Q1 2018
Contents
IEEE Circuits and Systems Magazine - Q1 2018 - Cover1
IEEE Circuits and Systems Magazine - Q1 2018 - Cover2
IEEE Circuits and Systems Magazine - Q1 2018 - Contents
IEEE Circuits and Systems Magazine - Q1 2018 - 2
IEEE Circuits and Systems Magazine - Q1 2018 - 3
IEEE Circuits and Systems Magazine - Q1 2018 - 4
IEEE Circuits and Systems Magazine - Q1 2018 - 5
IEEE Circuits and Systems Magazine - Q1 2018 - 6
IEEE Circuits and Systems Magazine - Q1 2018 - 7
IEEE Circuits and Systems Magazine - Q1 2018 - 8
IEEE Circuits and Systems Magazine - Q1 2018 - 9
IEEE Circuits and Systems Magazine - Q1 2018 - 10
IEEE Circuits and Systems Magazine - Q1 2018 - 11
IEEE Circuits and Systems Magazine - Q1 2018 - 12
IEEE Circuits and Systems Magazine - Q1 2018 - 13
IEEE Circuits and Systems Magazine - Q1 2018 - 14
IEEE Circuits and Systems Magazine - Q1 2018 - 15
IEEE Circuits and Systems Magazine - Q1 2018 - 16
IEEE Circuits and Systems Magazine - Q1 2018 - 17
IEEE Circuits and Systems Magazine - Q1 2018 - 18
IEEE Circuits and Systems Magazine - Q1 2018 - 19
IEEE Circuits and Systems Magazine - Q1 2018 - 20
IEEE Circuits and Systems Magazine - Q1 2018 - 21
IEEE Circuits and Systems Magazine - Q1 2018 - 22
IEEE Circuits and Systems Magazine - Q1 2018 - 23
IEEE Circuits and Systems Magazine - Q1 2018 - 24
IEEE Circuits and Systems Magazine - Q1 2018 - 25
IEEE Circuits and Systems Magazine - Q1 2018 - 26
IEEE Circuits and Systems Magazine - Q1 2018 - 27
IEEE Circuits and Systems Magazine - Q1 2018 - 28
IEEE Circuits and Systems Magazine - Q1 2018 - 29
IEEE Circuits and Systems Magazine - Q1 2018 - 30
IEEE Circuits and Systems Magazine - Q1 2018 - 31
IEEE Circuits and Systems Magazine - Q1 2018 - 32
IEEE Circuits and Systems Magazine - Q1 2018 - 33
IEEE Circuits and Systems Magazine - Q1 2018 - 34
IEEE Circuits and Systems Magazine - Q1 2018 - 35
IEEE Circuits and Systems Magazine - Q1 2018 - 36
IEEE Circuits and Systems Magazine - Q1 2018 - 37
IEEE Circuits and Systems Magazine - Q1 2018 - 38
IEEE Circuits and Systems Magazine - Q1 2018 - 39
IEEE Circuits and Systems Magazine - Q1 2018 - 40
IEEE Circuits and Systems Magazine - Q1 2018 - 41
IEEE Circuits and Systems Magazine - Q1 2018 - 42
IEEE Circuits and Systems Magazine - Q1 2018 - 43
IEEE Circuits and Systems Magazine - Q1 2018 - 44
IEEE Circuits and Systems Magazine - Q1 2018 - Cover3
IEEE Circuits and Systems Magazine - Q1 2018 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021Q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q1
https://www.nxtbookmedia.com