Physical Concepts and Basic Fluid Mechanics
61
3.2.4.2 Line Spectrum and Nyquist Criterion
The harmonic magnitudes of a typical aortic pressure pulse and aortic
flow pulse are shown in Fig. 3.2.3.
The magnitudes are small and
negligible beyond the tenth harmonic component. The Nyquist criterion
requires sampling frequency
of
at least twice the highest frequency
content in order to reconstruct the original waveform accurately. In the
present example, the tenth harmonic would be 1.5
x
10
or
15
Hz. The
minimal sampling frequency required is therefore 30 Hz. In most cases,
sampling frequency applied is much higher than this and typically at
100Hz. In other words, the pressure waveform is digitized at
10
msec
intervals.
3.2.4.3 Correlation, Coherence and Power Spectrum
Autocorrelation for a periodic function f(t) can be defined by
(3.2.3
1)
where
T
represents the time delay. Its power spectrum is given as
and inversely,
lT
TO
@,,(nu)
=
-
j41,(T)e-jnm7
(3.2.33)
(3.2.34)
Similarly, the cross-correlation for
two
functions fl(t) and f2(t) can be
defined
as:
