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.
Abstract: One of the primary uses of higher order statistics in
signal processing has been for detecting and estimation of non-
Gaussian signals in Gaussian noise of unknown covariance. This is
motivated by the ability of higher order statistics to suppress additive
Gaussian noise. In this paper, several methods to test for non-
Gaussianity of a given process are presented. These methods include
histogram plot, kurtosis test, and hypothesis testing using cumulants
and bispectrum of the available sequence. The hypothesis testing is
performed by constructing a statistic to test whether the bispectrum
of the given signal is non-zero. A zero bispectrum is not a proof of
Gaussianity. Hence, other tests such as the kurtosis test should be
employed. Examples are given to demonstrate the performance of the
presented methods.