IEEE Circuits and Systems Magazine - Q1 2018 - 16

Highest Remez Order that Can Be Practically Realized

350
400

300

350
250

300
250

200

200
150

150
100

100
50

80

0
5,000 4,500
4,000 3,500
3,000 2,500
2,000 1,500
1,000 500
FA + FF

60
X

40

Z

Y

50

20
-20log10min(δp, δs) in dB

(a)
Contour Map of Highest Remez Order that Can Be Practically
Realized Given Available Number of FA + FF and Target δp and δs

5,000

Hw Complexity = Total Number of Full
Adders (FA) + Number of Flip-Flops (FF)

4,500

350

4,000
300
3,500
250

3,000
2,500

200

2,000

150

1,500
100
1,000
50

500
20

30

40

50
60
70
-20log10min(δp, δs) in dB

80

90

100

(b)
Figure 4. contour maps of the practical bound in (11)-(12) ^a = 1 h illustrating the minimum hardware complexity (y-axis) that is
required in order to practically realize a specific remez order (color lines) of fIr filter given a target dp and ds.
16

IEEE cIrcuIts ANd systEMs MAgAzINE

fIrst quArtEr 2018



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