Direct analysis of non-quadratic phase coupling for detection of linearly modulated signals



Fidel Hernández Aitzol Iturrospe


The detection of a linearly modulated signal is currently accomplished by applying the Bispectrum. This technique is capable of detecting quadratic phase coupled spectral components, and consequently, can be used in order to reveal a linearly modulated signal presence. However, a linear modulation by itself does not exhibit quadratic phase coupled spectral analysis. Then, the application of the Bispectrum for detecting linearly modulated signals could be unsuccessful. In this paper a general method for detection of linearly modulated signals, which can be applied whether the signals comprise quadratic phase coupled spectral components or not, is proposed. This method is evaluated through numerical simulations and it is applied for detecting a local fault in rolling element bearings. The achieved results are compared with those obtained by the traditional spectral analysis and the Bispectrum, revealing the effectiveness obtained by the application of the proposed method.

How to Cite

Hernández, F., & Iturrospe, A. (2015). Direct analysis of non-quadratic phase coupling for detection of linearly modulated signals. Annual Conference of the PHM Society, 7(1).
Abstract 109 | PDF Downloads 68




Bouillaut, L., & Sidahmed, M. (2001). Etude des caractères non linéaires et cyclostationnaires des signaux vibratoires de boite de vitesse d'hélicoptère. Colloques sur le Traitement du Signal et des Images, GRETSI - Actes de Colloques.
Chaari, F., Bartelmus, W., Zimroz, R., Fakhfakh, T., & Haddar, M. (2012). Gearbox Vibration Signal Amplitude and Frequency Modulation. Journal Shock and Vibration 19 (4), p. 635-652.
Chen, H., & Zuo, M. (2009). Fault detection of gearbox with vibration signal analysis by a linear combination of adaptive wavelets. International Conference on Wavelet Analysis and Pattern Recognition, Baoding, China.
Fackrell, J., & McLaughlin, S. (1995). Quadratic phase coupling detection using higher order statistics. IEE Colloquium on Higher Order Statistics in Signal Processing: Are They of Any Use?, London, UK.
Gallego A., Urdiales, C., & Ruiz, D. (1999). Quadratic Phase Coupling Detection in Harmonic Vibrations via an Order-Recursive AR Bispectrum Estimation. Nonlinear Dynamics 19 (3), p. 273–294.
Hernández, F., & Caveda, O. (2008). The application of bispectrum on diagnosis of rolling element bearings: A theoretical approach. Mechanical Systems and Signal Processing 22 (3), p. 588–596.
Raad, A., & Sidahmed, M. (2002). Gear fault diagnosis using cyclic bispectrum. 15th Triennial IFAC World Congress, Barcelona, Spain.
Randall, R., & Antoni, J. (2011). Rolling element bearing diagnostics—A tutorial. Mechanical Systems and Signal Processing 25 (2), p. 485–520.
Rivola, A., & White, P. (1998). Detecting System Non- linearities by Means of Higher Order Statistics. Proceedings of the 3rd International Conference on Acoustical and Vibratory Surveillance Methods and Diagnostic Techniques, Senlis, France.
Sanaullah, M. (2013). A Review of Higher Order Statistics and Spectra in Communication Systems. Journal of Global Journal of Science Frontier Research Physics and Space Science 13 (4), p. 31–50.
Seydnejad, S. (2007). Detection of Nonlinearity in Cardiovascular Variability Signals using Cyclostationary Analysis. Annals of Biomedical Engineering 35 (5), p. 744–754.
Venkatakrishnan, P., Sukanesh, R. and Sangeetha, S. (2011). Detection of quadratic phase coupling from human EEG signals using higher order statistics and spectra. Journal of Signal, Image and Video Processing 5 (2), p. 217–229.
Technical Research Papers