On the application of matching pursuit decomposition to jet noise data

The Matching Pursuit decomposition is a signal processing technique that projects a signal onto a linear expansion of waveforms selected from a redundant set of arbitrary functions, collectively referred to as a Dictionary. A key feature of this method is its ability to reconstruct a signal using a carefully chosen subset of these waveforms. In the present paper, this method is applied to illustrate its potentialities for reduced-order modeling of jet noise data. The analysis is conducted on an experimental dataset containing pressure time series taken in both the near- and far-field of a compressible subsonic free jet. For this application, the Dictionary is constructed using Gabor functions, and it is shown that even with a very limited number of atoms (one thousand), significant physical properties of the near pressure field are preserved. The results demonstrate that the effects of Mach number, as well as radial and axial distances from the jet exit, are accurately reproduced in both spectral features and temporal correlations. In the frequency domain, the energy bump at the Kelvin-Helmholtz frequency is effectively captured, primarily in the region close to the jet exit. Additionally, the non-zero correlations between near- and far-field pressure fluctuations are correctly captured, along with the corresponding phase lag obtained from the correlation maxima. The analysis confirms that the Matching Pursuit decomposition adaptively selects atoms that best represent the original signals. The superposition of a limited number of these optimally chosen atoms provides a highly simplified yet physically meaningful representation of the complex original signals. Future developments and applications aimed at modeling jet noise sources and predicting acoustic radiation are also outlined.