54
Dynamics
of
the Vascular System
3.2
Frequency Domain and Fourier Analysis
3.2.1
Periodic Functions
A
periodic function with
a
period T, is defined by=
f(t>
=
f(t
+
T)
(3.2.1)
and it follows that:
f(t)
=
f(t
+
nT),n
=
O,fl,f2
.....
(3.2.2)
.....
.....
.....
.....
.....................
..........................
............................
..............................
Fig.
3.2.1
:
Measured aortic blood pressure waveforms showing periodicity. Oscillations
within systolic and diastolic pressure levels are slightly modulated by respiratory effects.
Figure 3.2-1
illustrates
the
periodic
blood
pressure
waveforms
oscillating within systolic and diastolic pressure levels with cardiac
period
T.
There is in general
a
slight change in pressure waveform
amplitudes due to the influence of respiration, i.e. inspiration and
expiration. In this case, we have for the pulsatile pressure waveforms:
pw
=
p(t
+
nT),n
=
O,+l,f2
.....
(3.2.3)
It is clear that any periodic signal satisfying the Dirichlet conditions
(convergence conditions) can be expressed by the Fourier series.
To
