
distance to any organic object in- or decreases. This 
change in resonance frequency is reflected in a 
change of voltage. This principle is used in homes in 
the form of touchless switches. However, since the 
changes in the tissue surface caused by pulse beat 
and respiration are very small, the use of classical 
LC oscillators is - apart from a few exceptions - not 
possible. Therefore a new nonlinear oscillator has 
been developed. With its help it is possible to 
measure changes in submillimeter range. Because of 
this high sensitivity even little muscle contractions 
will be detected by the sensor. As some of these 
minor contractions do belong to neither pulse nor 
respiration they have to be eliminated. It is 
necessary to filter and process the signal to eliminate 
these artifacts. An example for the measured signal 
is shown in Fig. 2. For more technical information 
please refer to (Jaeger, 2007). 
 
 
Figure 2: Signal measured by the sensor. 
2.3  Algorithms 
First the signal is band-filtered with hard coded cut-
off frequencies covering the whole spectrum of 
possible pulse and respiration frequencies. In the 
next step a low resolution FFT of this filtered signal 
is performed. In extreme cases the respiration 
frequency can be higher than the pulse frequency. 
Due to this there are four possible frequency bands 
(Fig.3): 
-  the whole frequency band from the lowest 
possible frequency of the respiration to the 
highest possible frequency of the pulse (WF) 
-  the lower frequency band of respiration 
from the lowest possible frequency of the 
respiration to the lowest possible frequency of 
the pulse (LF), 
-  the upper frequency band of pulse, from 
the highest possible frequency of the respiration 
to the highest possible frequency of the pulse 
(HF) 
-  and the overlapping band from the lowest 
possible frequency of the pulse to the highest 
possible frequency of the respiration (MF). 
By calculating relations between the different 
amplitudes, the frequency parts with high intensity 
can be discerned.  Normally there will be only two 
frequency parts with high intensity representing 
pulse and respiration. 
 
 
Figure 3: Spectrum of the filtered signal with four 
frequency bands. 
If there are more than two such frequency parts, 
there has to be a measurement error. If no error is 
detected the frequency parts defined above can be 
analyzed further. If there is a frequency part of high 
intensity in the lower frequency band of respiration, 
there may be only one such frequency part in the 
overlapping band - the one of the pulse. If such a 
frequency part is additionally detected in the upper 
frequency band of the pulse there cannot be any in 
the overlapping band. As soon as these conditions 
are met, the frequencies for pulse and respiration are 
approximately determined. With the detected 
frequencies it is possible to define narrow cut-off 
frequencies for pulse and respiration. With these 
cut-off frequencies the input signal is filtered again, 
once for pulse and once for respiration. 
After this step there are two rather clear signals 
which are relatively free of errors.
  With these 
filtered signals it is possible to determine more exact 
frequencies for pulse and respiration. Therefore the 
filtering is designed to adapt which means that the 
cut-off frequencies of the fine filters are always 
readjusted using the frequencies determined by the 
fine filtered signals. Additionally the approximated 
frequencies of pulse and respiration gained from the 
roughly filtered input signal are used to validate the 
adjustment of the cut-off frequencies for the fine 
filters. The determination of the frequency of the 
fine filtered signal works as follows: On the one 
hand zero-crossings are counted using a hysteresis, 
on the other hand a high resolution FFT for the 
filtered signals is processed. Both results undergo a 
plausibility check. 
The frequency determination by counting zero-
crossings is done by using hysteresis. A zero-
crossing is only interpreted as such if the signal does 
not only drop below a lower hysteresis border but 
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