
where
b
0
¼ KK
c
K
A
v
2
n
z, b
1
¼ KK
c
K
A
(1 þ t
A
z)v
2
n
, b
2
¼ KK
c
K
A
v
2
n
t
A
(8:252)
a
0
¼ KK
c
K
A
v
2
n
z,
a
1
¼ KK
c
K
A
v
2
n
z þ K
c
v
2
n
z(1 þ KK
A
K
_
u
),
a
2
¼ KK
c
K
A
v
2
n
t
A
þ K
c
2zv
n
z þ v
2
n
þ KK
A
K
_
u
v
2
n
(1 þ t
A
z)
a
3
¼ K
c
z þ 2zv
n
K
c
þ v
2
n
p
1
p
2
þ KK
c
K
A
K
_
u
t
A
v
2
n
a
4
¼ K
c
þ 2zv
n
p
1
p
2
þ v
2
n
(p
1
þ p
2
)
a
5
¼ p
1
p
2
þ 2zv
n
(p
1
þ p
2
) þ v
2
n
a
6
¼ p
1
þ p
2
þ 2zv
n
9
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
=
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
;
(8:253)
An equivalent implementation of the system with transfer function in Equation 8.251 consists of the
input u
com
(t) feeding parallel first- and second-order components with the outputs of each block
summed to generate the pitch response u(t). Partial fraction expansion of Equation 8.251 using
numerical values for b
0
, b
1
, b
2
, and a
0
, a