Digital Signal Processing Reference
In-Depth Information
Figure 7.4
Lowpass filter specification.
+
Ω
1
c
∫
j
(
n
−τ
)
Ω
h
(
n
)
=
e
⋅
d
Ω
,
(7.14)
LP
2
π
−
Ω
c
n
=
0
1
…
,
2
M
]
[
sin
(
n
−
τ
)
Ω
⎧
c
,
for
n
≠
τ
⎪
⎨
(
n
−
τ
)
π
⎪
h
(
n
)
=
LP
⎪
⎩
Ω
/
π
,
for
n
=
τ
c
⎪
n
=
0
1
…
,
2
M
(7.15)
Figure 7.5
Highpass filter specification.
⎡
⎤
−
Ω
+
π
1
c
j
(
n
−
τ
)
Ω
j
(
n
−
τ
)
Ω
⎢
⎣
∫
∫
⎥
⎦
h
(
n
)
=
e
⋅
d
Ω
+
e
⋅
d
Ω
HP
2
π
⎢
⎥
−
π
Ω
c
n
=
0
1
…
,
2
M
(7.16)
]
]
[
[
⎧
sin
(
n
−
τ
)
π
−
sin
(
n
−
τ
)
Ω
c
,
for
n
≠
τ
⎪
⎨
(
n
−
τ
)
π
⎪
h
(
n
)
=
HP
⎪
⎩
(
π
-
Ω
)
/
π
,
for
n
=
τ
c
⎪
n
=
0
1
…
,
2
M
(7.17)
