58
Dynamics
of the
Vascular System
3.2.3 Complex Form of Fourier Series
By
expressing sine and cosine in terms
of
exponentials, we have
(3.2.15)
cos(nw,t)
=
-(e
1
;nw,,i
+
e-;n~~l
)
2
(3.2.16)
and substituting into
N
f(t)
=
a,
+
x[(a,
cos(nw,t)
+
bn
sin(nw,t)]
(3.2.17)
n=l
we have
(3.2.18)
1
-
JfloOl
-jb,)e”’uOi
+-(a,
+
jbn)e
2
or simply:
(3.2.19)
n=l
where
(3.2.20)
1
lT
2
*0
c,
=
-a,
=
-
ff(t)dt
(3.2.21)
