Solution: 9.10.4.1
H = (1;T
d
)
1
T
c
=
1;
d
d
t
t
=
d
;
d
d
t
t
=
(
d
;
d
)
t
t
d
Then the degree (or order) of the numerator is
deg(
d
;
d
)+(deg)(
t
);;
and the degree of the denominator of H is
deg(
t
)+(deg)(
d
);;
Thus for H to haveapolezero excess of zero or greater wemust have
deg(
d
;
d
)+(deg)(
t
) deg(
t
)+(deg)(
d
):
Similarly,
G
c
=
T
c
T
d
1
G
p
=
t
d
p
d
d
p
:
Then the degree (or order) of the numerator of G
c
is
deg(
d
)+deg(
d
)+deg(
p
);;
and the degree of the denominator of G
c
is
deg(
d
)+(deg)(
p
)+deg(
d
):
Thus for G
c
to haveapole zero excess of zero or greater wemust have
deg(
d
)+deg(
d
)+deg(
p
) deg(
d
)+(deg)(
p
)+deg(
d
):
1