{"title":"Signal Reconstruction Using Cepstrum of Higher Order Statistics","authors":"Adnan Al-Smadi, Mahmoud Smadi","volume":6,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":280,"pagesEnd":286,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/15863","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.<\/p>\r\n","references":"[1] A. Al-Smadi, \"Cumulant-Based Order Selection of Non-Gaussian\r\nAutoregressive Moving Average Models: The Corner Method,\" Signal\r\nProcessing, vol. 85, pp. 449-456, 2005.\r\n[2] A. Al-Smadi and M. Smadi, \"Phase and Magnitude Extraction using\r\nCepstrum and Higher Order Statistics,\" 10th IEEE International\r\nConference on Electronics, Circuits and Systems, pp. 52-55, 2003.\r\n[3] A. Al-Smadi and M. Smadi, \"Study of the Reliability of a Binary\r\nSymmetric Channel under Non-Gaussian Disturbances,\" International\r\nJournal of Communication Systems, vol. 16, pp. 865-973, 2003.\r\n[4] A. Al-Smadi and D.M. Wilkes, \"Robust and Accurate ARX and ARMA\r\nModel Order Estimation of Non-Gaussian Processes,\" IEEE Trans. On\r\nSignal Processing, vol. 50, pp.759 -763, 2002.\r\n[5] S. Alshebeili, A. Cetin, and A. Venetsanopoulos, \"Identification of\r\nnonminimum phase MA systems using cepstral operations on slices of\r\nhigher order spectra,\" IEEE Trans. On Circuits and Systems II: Analog\r\nand Digital Signal Processing, vol. 39, pp. 634-637, 1992.\r\n[6] B.P. Bogert, M. Healy, and J. Tukey, \"The quefrency analysis of time\r\nseries for echoes: cepstrum, pseudo-autocovariance, cross-cepstrum, and\r\nsaphe cracking,\" Proc. Symposium time series analysis, pp. 209-243,\r\n1963.\r\n[7] B.P. Bogert and J. Ossana, \"The heuristic of cepstrum analysis of a\r\nstationary complex echoed Gaussian signal in stationary Gaussian\r\nnoise,\" IEEE Trans. Inform. Theory, vol. 72, pp. 373-380, 1966.\r\n[8] T.J. Cavicchi, Digital Signal Processing. New York: John Wiley, 2000.\r\n[9] C.Y. Chi, \"Fourier Series based nonminimum phase model for statistical\r\nsignal processing,\" IEEE Trans. On Signal Processing, vol. 47pp. 2228-\r\n2240, 1999.\r\n[10] D.G. Childers, Speech Processing and Synthesis Toolboxes. New York:\r\nJohn Wiley, 2000.\r\n[11] J.M. Mendel, \"Tutorial on higher-order statistics (spectra) in signal\r\nprocessing and system theory: Theoretical results and some\r\napplications,\" Proceedings of the IEEE, vol. 79, pp. 278-305, 1991.\r\n[12] C.L. Nikias and M.R. Raghuveer, \"Bispectrum estimation: A digital\r\nsignal processing framework,\" Proceedings of the IEEE, vol. 75, pp.\r\n869-891, 1987.\r\n[13] A.V. Oppenheim and R.W. Schafer, Discrete Time Signal Processing.\r\nNew Jersey: Prentice Hall, 1989.\r\n[14] R. Pan and C.L. Nikias, \"The complex cepstrum of higher-order\r\ncumulants and nonminimum phase identification,\" IEEE Trans. On\r\nAcoust., Speech, and Signal Processing, vol. 36, pp. 186-205, 1988.\r\n[15] A.P. Petropulu and C.L. Nikias, \"Blind deconvolution of coloured\r\nsignals based on higher-order cepstra and data fusion. IEE Proceedings-\r\nF, vol. 140: 356-361, 1993.\r\n[16] A.P. Petropulu and C.L. Nikias, \"The complex cepstrum and bicepstrum:\r\nAnalytic performance evaluation in the presence of Gaussian noise,\"\r\nIEEE Trans.On Acoust. Speech, and Signal Processing, vol. 38, pp.\r\n1246-1256, 1990.\r\n[17] J. Proakis and Manolakis, Digital Signal Processing. New Jersey:\r\nPrentice Hall, 1996.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 6, 2007"}