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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