Physical
Concepts
and Basic Fluid Mechanics
55
apply the Fourier series, periodicity and linearity need to be satisfied.
Periodicity is often observed, because cardiac period is varies little from
beat to beat during a short interval.
3.2.2 Trigonometric Fourier Series
A
periodic function can be expressed in terms of its sine and cosine
components:
f
(t)
=
a,
+
a,
cosw,t
+
a2
cos2wOt
+
.....
+
b,
sinw,t
+
b2
sin2wot
+ .
....
(3.2.4)
which is
N
f
(t)
=
a,
+
x[(a,,
cos(nwot)
+
b,,
sin(nw,t)]
(3.2.5)
n=l
where the Fourier coefficients are:
IT
TO
a,
=
-
If
(t)dt
(3.2.6)
2T
TO
b,,
=
-
If
(t)sin(nco,t)dt
2n
T
w0=2#-=-
(3.2.8)
(3.2.9)
where
coo
is the angular frequency,fo
is
the fundamental frequency and
T
is the period, n is the nth number of harmonics and
N
is the total number
of harmonics in the Fourier series summation.
