Modulation Analysis of Cavitation Noise

Cavitation noise is produced by the formation and collapse of bubbles on the surface of underwater propellers. Acoustic recordings of cavitation noise are broadband and noise-like, yet distinctly rhythmic as the propeller blades rotate through water flow inhomogeneities. With Prof. Les Atlas (UWEE) and Dr. Ivars Kirsteins (NUWC), our goal is to develop maximum-likelihood demodulation algorithms for characterizing the rhythmic components of cavitation noise. By treating the carrier as a stationary noise signal, the maximum-likelihood approach precisely defines what modulations can and can't be detected from a random process.

  • P. Clark, I. Kirsteins and L. Atlas, "Multiband analysis for colored amplitude-modulated ship noise," Proc. IEEE ICASSP, Dallas, TX, 2010. [poster (PDF)]
Photographs of cavitating propellers.

Modulation spectrum of actual cavitation data, showing the fundamental propeller rate of 2.8 Hz with varying intensity depending on carrier (acoustic) frequency.

Modulation Toolbox v2.1 for MATLAB

The Modulation Toolbox is a set of MATLAB files for analyzing and modifying modulation spectra in speech, music and natural sounds. It grew out of my MSEE thesis on coherent modulation filtering, a form of signal modification that operates on the envelope fluctuations of an audio signal without changing its "fine structure." Modulation filtering is a tool with potential applications including speech enhancement, source separation, and audio compression. You can download the toolbox here.

So what are "envelopes" and "fine structure?" These are terms typically associated with, respectively, the slow amplitude modulations of subband signals and whatever is left over. Coherent demodulation, however, defines modulator signals relative to bandlimited carriers in a signal-adaptive way. A disciplined approach to signal modeling allows us to define consistent and distortion-free modulation filters, and challenges the widespread use of the Hilbert envelope. For more details see:
  • P. Clark and L. Atlas, "A sum-of-products model for effective coherent modulation filtering," Proc. IEEE ICASSP, Taipei, 2009. [poster (PDF)]
  • P. Clark and L. Atlas, "Time-Frequency Coherent Modulation Filtering of Nonstationary Signals" Trans. Signal Process., vol. 57, no. 11, pp. 4323-4332, November 2009.
A conceptual demonstration of demodulation methods. In the non-coherent method, the envelope (red, upper-left) is assumed to be positive and the resulting carrier (blue, upper-right) contains a bandwidth-expanding discontinuity. In coherent demodulation, both the carrier (blue, lower-left) and the resulting modulator (red, lower-right) are bandlimited signals. Although shown here as real signals, coherent modulators and carriers are generally complex-valued.