Chapter 10
10.1 To compute the filter orders, we use Kaiser’s formula of Eq. (10.3), Bellanger’s formula
of Eq. (10.4), and Hermann’s formula of Eq. (10.5).
Filter #1:
Kaiser’s formula -
(
)
()
158097.157
2/10625.014375.06.14
1300012.00224.0log20
10
≈=
−
−⋅−
=
πππ
N
Bellanger’s formula -
(
)
()
163575.1621
2/10625.014375.03
000112.00224.010log2
10
≈=−
−
⋅
⋅
−
=
πππ
N
Hermann’s formula -
()
()
(
)
[
]
()()
[]
8326.24278.00224.0log5941.00224.0log00266.0
000112.0log4761.00224.0log07114.00224.0log005309.0,
10
2
10
1010
2
10
=++
−⋅−+=
∞ sp
D
δδ
(
)
[
]
1913.12000112.0log0224.0log51244.001217.11,
1010
=
−
+=
sp
F
δ
δ
()
[]
()
1518434.150
2/10625.014375.0
2/10625.014375.01913.128326.2
2
≈=
−
−−
=
πππ
πππ
N
Filter #2:
Kaiser’s formula -
(
)
()
34186.33
2/2075.02875.06.14
13034.0017.0log20
10
≈=
−
−⋅−
=
πππ
N
Bellanger’s formula -
(
)
()
373012.361
2/2075.02875.03
034.0017.010log2
10
≈=−
−
⋅
⋅
−
=
πππ
N
Hermann’s formula -
()
()
(
)
[
]
()()
[]
474777.14278.0017.0log5941.0017.0log00266.0
034.0log4761.0017.0log07114.0017.0log005309.0,
10
2
10
1010
2
10
=++
−⋅−+=
∞ sp
D
δδ
(
)
[
]
85791019.10034.0log017.0log51244.001217.11,
1010
=
−
+=
sp
F
δ
δ
()
[
]
()
37435.36
2/2075.02875.0
2/2075.02875.085791019.10474777.1
2
≈=
−
−−
=
πππ
πππ
N
Filter #3:
Kaiser’s formula -
(
)
()
126107.11
2/345.0575.06.14
130137.00411.0log20
10
≈=
−
−⋅−
=
πππ
k
N
Bellanger’s formula -
(
)
()
1304.121
2/345.0575.03
0137.00411.010log2
10
≈=−
−
⋅
⋅
−
=
πππ
N
Hermann’s formula -
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