Optimization of Parametric Periodograms for the Study of Density Fluctuations in a Supersonic Jet
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the minimum in the graph vs p. To do so, we had
to choose the frequency resolution
2
wp
σ
Δ. This choice is
simple when the signals are well known as in the first
example. The four frequencies of the original signal were
clearly identified. For the second example, where the
signal is random, the resolution depends on previous
knowledge of the experiment. In our case, entropic and
acoustic peaks expected from the literature, were re-
solved. Furthermore, a third low frequency non expected
peak, was studied with respect to the position in the jet
where the signal came from.
This paper gives a more objective way to determine
the number of parameters and a better spectral density. It
is surprising that even though it is well known that high
temporal resolution implies low frequency resolution, wh en
sampling a signal, the Nyquist theorem is applied blindly
without taking into accoun t the final use of the data. This
is an important result in signal processing that can be
seen by comparing Figure 7 with Figure 11.
A Rayleigh scattering technique combined with the
heterodyne detection of light scattered by the molecules
of a transparent gas was used to detect density fluctua-
tions. The periodograms helped resolve various frequent-
cies and gave more insight on the internal structure of the
jet.
The periodograms are parametric signal processing
tools that allow the modeling of a signal. To properly
implement them, it is necessary to determine the optimal
number of parameters, which ensures that the signal has
been modeled correctly. The theory predicts that many
parameters could add spurious peaks, and that few pa-
rameters may not reproduce the signal properly. The
results presented in this paper show that the resolu-
tion
Δcould be an important factor in finding the opti-
mal number of parameters required to model a signal by
using param e t ri c periodograms.
In the future, we expect to determine clearly how to
obtain the optimal number of parameters directly from
the frequency resolution .
7. Acknowledgements
To the PAPIIT IN117712 project “Propagación de ondas
a través de interfaces”.
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