Optimization of Parametric Periodograms for the Study of Density Fluctuations in a Supersonic Jet

Abstract

In our research on the density fluctuations of a supersonic jet we were confronted with a quite difficult problem. In the power spectrum obtained either with a spectrum analyzer, the peaks of the two of the modes that we wanted to identify overlapped. We needed to find a signal processing method that would resolve the two main frequencies. We made a thorough investigation of several methods and thought that parametric periodograms were the appropriate tool. The use of parametric periodograms in signal processing requires constant training. The proper application of this tool depends on the determination of the number of parameters that has to be used to best model a real signal. The methods generally used to determine this number are subjective, depending on trial and error and on the experience of the user. Some of these methods rely on the minimization of the estimated variance of the linear prediction error , as a function of the number of parameters n. In many cases, the graph vs n doesn’t have a minimum, and the methods cannot be used. In this paper, we show that there is a strong relationship between and the frequency resolution . That is, as we modify , we obtain graphs of vs n that present at least one minimum. The spectrum obtained with this optimal number of parameters, always reproduces the frequency information of the original signal. In this paper, we present basically the signal processing of the data obtained in a Rayleigh scattering experiment on a supersonic jet that has also been designed by the authors.