Detection of Periodic Signals in Noise Based on Higher-Order Statistics Joined to Convolution Process and Spectral Analysis

  • Miguel Enrique Iglesias Martínez
  • Fidel Ernesto Hernández Montero
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8258)


This paper refers to the application of higher-order statistical signal processing techniques (cumulant calculation) on Gaussian noise cancellation. The performed procedure, joined to a convolution process and Fast Fourier Transform (FFT) application, results in the complete estimation (i.e., amplitude, frequency and phase recovery) of any corrupted periodic signal. Whereas tone frequency estimation is performed by 4th-order cumulant calculation, phase recovery is achieved by the convolution of the cumulant calculation and the corrupted signal. At last, the original signal amplitude is recovered by means of modification of the resulting amplitude spectrum. In this paper, higher-order statistics foundations are presented and the validation of the proposed algorithm is revealed in both theoretical and practical sense. Obtained results are highly satisfactory.


Higher-Order Statistics Noise Cancellation Convolution Fourier Transform 


  1. 1.
    Howard, R.M.: Principles of Random Signal Analysis and Low Noise Design. John Wiley & Sons Ltd. (2009)Google Scholar
  2. 2.
    Swami, A., Mendel, J.M.: Cumulant-Based Approach to the Harmonic Retrieval Problem. In: International Conference on Acoustics, Speech, and Signal Processing, ICASSP 1988, April 11-14, vol. 4, pp. 2264–2267 (1988)Google Scholar
  3. 3.
    Swami, A., Mendel, J.M.: Cumulant-Based Approach to Harmonic Retrieval and Related Problems. IEEE Transactions on Signal Processing 39(5), 1099–1109 (1991)CrossRefGoogle Scholar
  4. 4.
    Le, T.H., Clediere, J., Serviere, C., Lacoume, J.L.: Noise Reduction in Side Channel Attack Using Fourth-Order Cumulant. IEEE Transactions on Information Forensics and Security 2(4), 710–720 (2007)CrossRefGoogle Scholar
  5. 5.
    Zhang, Y., Wang, S.-X.: A Hybrid Approach to Harmonic Retrieval in Non-Gaussian Noise Using Fourth-Order Moment and Autocorrelation. In: Fourth International Conference on Signal Processing, ICSP 1998, vol. 1, pp. 411–414 (1998)Google Scholar
  6. 6.
    Blagouchine, I.V., Moreau, E.: Unbiased Adaptive Estimations of the Fourth-Order Cumulant for Real Random Zero-Mean Signal. IEEE Transactions on Signal Processing 57(9), 3330–3346 (2009)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Narasimhan, S.V., Basumallick, N., Chaitanya, R.: Improved Phase Estimation Based on Complete Bispectrum and Modified Group Delay. Signal, Image and Video Processing 2(3), 261–274 (2008)CrossRefzbMATHGoogle Scholar
  8. 8.
    Geng, M., Liang, H., Wang, J.: Research on Methods of Higher-order Statistics for Phase Difference Detection and Frequency Estimation. In: 4th International Congress on Image and Signal Processing, Shanghai, vol. 4, pp. 2189–2193 (2011)Google Scholar
  9. 9.
    Sacchi, M.D., Ulrych, T.J., Walker, C.J.: Interpolation and extrapolation using a high-resolution discrete Fourier transform. IEEE Transactions on Signal Processing 46(1), 31–38 (1998)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kachenoura, A., Albera, L., Bellanger, J.-J., Senhadji, L.: Non-Minimum Phase Identification Based on Higher Order Spectrum Slices. IEEE Transactions on Signal Processing 56(5), 1821–1829 (2008)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Nikias, C.L., Mendel, J.M.: Signal Processsing with Higher-Order Spectra. IEEE Signal Processing Magazine 10(3), 10–37 (1993)CrossRefGoogle Scholar
  12. 12.
    Molí, S., Josep M.: Técnicas de Speech Enhancement Considerando Estadísticas de Orden Superior, Tesis Doctoral, Barcelona, Junio (1995),

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Miguel Enrique Iglesias Martínez
    • 1
  • Fidel Ernesto Hernández Montero
    • 1
  1. 1.Departamento de TelecomunicacionesUniversidad de Pinar del Río Hermanos Saíz Montes de OcaPinar del RíoCuba

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