Digital Signal Processing Reference
In-Depth Information
These functions are used in the calculation of the pole-zero locations in the next
section.
1
H
[
j
(
ω
/
ω
)]
=
(2.55)
E
,
n
o
2
2
1
+
ε
⋅
R
(
ω
/
ω
)
n
o
where ε is as defined previously.
−
0
⋅
a
ε
=
10
pass
−
1
(2.56)
φ
2
2
−
1
/
2
∫
u
(
φ
,
k
)
=
(
−
k
sin
x
)
dx
(2.57)
0
sn
(
u
,
k
)
=
sin(
φ
)
(2.58)
cn
(
u
,
k
)
=
cos(
φ
)
(2.59)
sc
(
u
,
k
)
=
tan(
φ
)
(2.60)
d
φ
dn
(
u
,
k
)
=
(2.61)
du
The complete elliptic integral of the first kind will be used more often than the
incomplete integral and it is defined in (2.62). It should be noted at this point that
there are various ways to define the elliptic integrals and elliptic functions. Some
authors use the modulus
k
as we have in this text, while others use other
parameters related to
k
.
π
/
2
∫
2
2
−
1
/
2
CEI
(
k
)
=
u
(
π
/
2
k
)
=
(
−
k
sin
x
)
dx
(2.62)
0
