Signal Reconstruction Using Cepstrum of Higher Order Statistics
This paper presents an algorithm for reconstructing phase and magnitude responses of the impulse response when only the output data are available. The system is driven by a zero-mean independent identically distributed (i.i.d) non-Gaussian sequence that is not observed. The additive noise is assumed to be Gaussian. This is an important and essential problem in many practical applications of various science and engineering areas such as biomedical, seismic, and speech processing signals. The method is based on evaluating the bicepstrum of the third-order statistics of the observed output data. Simulations results are presented that demonstrate the performance of this method.
[1] A. Al-Smadi, "Cumulant-Based Order Selection of Non-Gaussian
Autoregressive Moving Average Models: The Corner Method," Signal
Processing, vol. 85, pp. 449-456, 2005.
[2] A. Al-Smadi and M. Smadi, "Phase and Magnitude Extraction using
Cepstrum and Higher Order Statistics," 10th IEEE International
Conference on Electronics, Circuits and Systems, pp. 52-55, 2003.
[3] A. Al-Smadi and M. Smadi, "Study of the Reliability of a Binary
Symmetric Channel under Non-Gaussian Disturbances," International
Journal of Communication Systems, vol. 16, pp. 865-973, 2003.
[4] A. Al-Smadi and D.M. Wilkes, "Robust and Accurate ARX and ARMA
Model Order Estimation of Non-Gaussian Processes," IEEE Trans. On
Signal Processing, vol. 50, pp.759 -763, 2002.
[5] S. Alshebeili, A. Cetin, and A. Venetsanopoulos, "Identification of
nonminimum phase MA systems using cepstral operations on slices of
higher order spectra," IEEE Trans. On Circuits and Systems II: Analog
and Digital Signal Processing, vol. 39, pp. 634-637, 1992.
[6] B.P. Bogert, M. Healy, and J. Tukey, "The quefrency analysis of time
series for echoes: cepstrum, pseudo-autocovariance, cross-cepstrum, and
saphe cracking," Proc. Symposium time series analysis, pp. 209-243,
1963.
[7] B.P. Bogert and J. Ossana, "The heuristic of cepstrum analysis of a
stationary complex echoed Gaussian signal in stationary Gaussian
noise," IEEE Trans. Inform. Theory, vol. 72, pp. 373-380, 1966.
[8] T.J. Cavicchi, Digital Signal Processing. New York: John Wiley, 2000.
[9] C.Y. Chi, "Fourier Series based nonminimum phase model for statistical
signal processing," IEEE Trans. On Signal Processing, vol. 47pp. 2228-
2240, 1999.
[10] D.G. Childers, Speech Processing and Synthesis Toolboxes. New York:
John Wiley, 2000.
[11] J.M. Mendel, "Tutorial on higher-order statistics (spectra) in signal
processing and system theory: Theoretical results and some
applications," Proceedings of the IEEE, vol. 79, pp. 278-305, 1991.
[12] C.L. Nikias and M.R. Raghuveer, "Bispectrum estimation: A digital
signal processing framework," Proceedings of the IEEE, vol. 75, pp.
869-891, 1987.
[13] A.V. Oppenheim and R.W. Schafer, Discrete Time Signal Processing.
New Jersey: Prentice Hall, 1989.
[14] R. Pan and C.L. Nikias, "The complex cepstrum of higher-order
cumulants and nonminimum phase identification," IEEE Trans. On
Acoust., Speech, and Signal Processing, vol. 36, pp. 186-205, 1988.
[15] A.P. Petropulu and C.L. Nikias, "Blind deconvolution of coloured
signals based on higher-order cepstra and data fusion. IEE Proceedings-
F, vol. 140: 356-361, 1993.
[16] A.P. Petropulu and C.L. Nikias, "The complex cepstrum and bicepstrum:
Analytic performance evaluation in the presence of Gaussian noise,"
IEEE Trans.On Acoust. Speech, and Signal Processing, vol. 38, pp.
1246-1256, 1990.
[17] J. Proakis and Manolakis, Digital Signal Processing. New Jersey:
Prentice Hall, 1996.
[1] A. Al-Smadi, "Cumulant-Based Order Selection of Non-Gaussian
Autoregressive Moving Average Models: The Corner Method," Signal
Processing, vol. 85, pp. 449-456, 2005.
[2] A. Al-Smadi and M. Smadi, "Phase and Magnitude Extraction using
Cepstrum and Higher Order Statistics," 10th IEEE International
Conference on Electronics, Circuits and Systems, pp. 52-55, 2003.
[3] A. Al-Smadi and M. Smadi, "Study of the Reliability of a Binary
Symmetric Channel under Non-Gaussian Disturbances," International
Journal of Communication Systems, vol. 16, pp. 865-973, 2003.
[4] A. Al-Smadi and D.M. Wilkes, "Robust and Accurate ARX and ARMA
Model Order Estimation of Non-Gaussian Processes," IEEE Trans. On
Signal Processing, vol. 50, pp.759 -763, 2002.
[5] S. Alshebeili, A. Cetin, and A. Venetsanopoulos, "Identification of
nonminimum phase MA systems using cepstral operations on slices of
higher order spectra," IEEE Trans. On Circuits and Systems II: Analog
and Digital Signal Processing, vol. 39, pp. 634-637, 1992.
[6] B.P. Bogert, M. Healy, and J. Tukey, "The quefrency analysis of time
series for echoes: cepstrum, pseudo-autocovariance, cross-cepstrum, and
saphe cracking," Proc. Symposium time series analysis, pp. 209-243,
1963.
[7] B.P. Bogert and J. Ossana, "The heuristic of cepstrum analysis of a
stationary complex echoed Gaussian signal in stationary Gaussian
noise," IEEE Trans. Inform. Theory, vol. 72, pp. 373-380, 1966.
[8] T.J. Cavicchi, Digital Signal Processing. New York: John Wiley, 2000.
[9] C.Y. Chi, "Fourier Series based nonminimum phase model for statistical
signal processing," IEEE Trans. On Signal Processing, vol. 47pp. 2228-
2240, 1999.
[10] D.G. Childers, Speech Processing and Synthesis Toolboxes. New York:
John Wiley, 2000.
[11] J.M. Mendel, "Tutorial on higher-order statistics (spectra) in signal
processing and system theory: Theoretical results and some
applications," Proceedings of the IEEE, vol. 79, pp. 278-305, 1991.
[12] C.L. Nikias and M.R. Raghuveer, "Bispectrum estimation: A digital
signal processing framework," Proceedings of the IEEE, vol. 75, pp.
869-891, 1987.
[13] A.V. Oppenheim and R.W. Schafer, Discrete Time Signal Processing.
New Jersey: Prentice Hall, 1989.
[14] R. Pan and C.L. Nikias, "The complex cepstrum of higher-order
cumulants and nonminimum phase identification," IEEE Trans. On
Acoust., Speech, and Signal Processing, vol. 36, pp. 186-205, 1988.
[15] A.P. Petropulu and C.L. Nikias, "Blind deconvolution of coloured
signals based on higher-order cepstra and data fusion. IEE Proceedings-
F, vol. 140: 356-361, 1993.
[16] A.P. Petropulu and C.L. Nikias, "The complex cepstrum and bicepstrum:
Analytic performance evaluation in the presence of Gaussian noise,"
IEEE Trans.On Acoust. Speech, and Signal Processing, vol. 38, pp.
1246-1256, 1990.
[17] J. Proakis and Manolakis, Digital Signal Processing. New Jersey:
Prentice Hall, 1996.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:64853", author = "Adnan Al-Smadi and Mahmoud Smadi", title = "Signal Reconstruction Using Cepstrum of Higher Order Statistics", abstract = "This paper presents an algorithm for reconstructing phase and magnitude responses of the impulse response when only the output data are available. The system is driven by a zero-mean independent identically distributed (i.i.d) non-Gaussian sequence that is not observed. The additive noise is assumed to be Gaussian. This is an important and essential problem in many practical applications of various science and engineering areas such as biomedical, seismic, and speech processing signals. The method is based on evaluating the bicepstrum of the third-order statistics of the observed output data. Simulations results are presented that demonstrate the performance of this method.
", keywords = "Cepstrum, bicepstrum, third order statistics", volume = "1", number = "6", pages = "290-6", }
