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. Keywords—Non-Gaussian, bispectrum, kurtosis, hypothesis testing, histogram. I. INTRODUCTION NDOUBTEDLY, the most widely used model for the distribution of a random variable is the Gaussian distribution. That is because it is simple, tractable, and fairly realistic model; i.e., the Gaussian process has many properties that make analytic results possible. It also describes several types of physical phenomena that are usually confirmed by experiments. Furthermore, the central limit theorem provides the mathematical justification for using the Gaussian distribution as a model for a large number of different physical phenomena in which the observed random variable is the result of a large number of individual random processes [1]. These reasons make the Gaussian process very fundamental and important in engineering and science problems. A random process is Gaussian if every finite set of {y(n)} is a Gaussian (Normal) random vector. Normal probabilistic distribution in many cases describes what normally happens, especially when sums of large numbers of random variables are involved. Gaussian entities are the foundation of basic stochastic signal processing. The slope of the Gaussian is the proverbial bell curve. The Gaussian random process is known as a second order process because its probability density function (PDF) and therefore all its statistical properties are completely determined by the first and second moments; that is, by the mean and the variance which are the sole parameters of the process. Hence, the information contained in the power Manuscript received September 26, 2005. A. Al-Smadi is with the Department of Electronics Engineering, Hijjawi Faculty for Engineering Technology, Yarmouk University, Irbid 21163, Jordan (e-mail: smadi98@yahoo.com or smadi98@yu.edu.jo). spectrum is essentially that which is present in the autocorrelation sequence. The first 1 and second order statistics are popular signal processing tools. These tools have been used extensively for the analysis of process data. It is a well- known fact that second order statistics are phase-blind; that is, they are able to describe minimum-phase systems only. The second order measures work fine if the signal has a Gaussian PDF. The information contained in the second order statistics (SOS), or autocorrelation, suffices for the statistical description of Gaussian process. However, many real-life signals are non-Gaussian. For example, the electromagnetic environment encountered by receiver systems is often non- Gaussian in nature. However, the receiving systems are designed to perform in white Gaussian noise [2]. Also, acoustic noise is in many cases highly non-Gaussian. In addition, biological signals typified by electroencephalograms (EEG) or electromyograms (EMG) are non-Gaussian [13]. Hence, in practice, there are situations where we must look beyond the autocorrelation of the available data to suppress additive noise, extract phase information, or obtain information regarding deviations from Gaussianness. This necessitates the use of higher order statistics (HOS) tools. HOS techniques were first proposed over four decades ago [3, 4]. While the Gaussian random process still plays a great and significant role in stochastic signal processing, non-Gaussian random processes and HOS, or cumulants, are of increasing importance to the researchers. Higher order (≥3) cumulants of non-Gaussian measurements contain not only the amplitude but also phase information of the unknown system. Furthermore, they are insensitive to Gaussian noise since all higher order (≥3) cumulants of Gaussian random processes are equal to zero. HOS measures are extensions of second order measures to higher orders; i.e., extension of autocorrelation for multiple lags. Applications of HOS have been found in diverse of fields such as speech, seismic data processing, plasma physics, optics, and economics [5]. As the field of HOS progresses, more accurate and sophisticated algorithms and techniques are revealed. In fact, the use of HOS may well be one of the new frontiers in signal processing, communications, statistical data analysis, and many other related fields. The study of detection and estimation in non-Gaussian process is important for many applications. Examples include radars which must operate in high clutter environments and sonar systems operating in the presence of high reverberation [14]. Tests for Gaussianity of a Stationary Time Series Adnan Al-Smadi U World Academy of Science, Engineering and Technology International Journal of Electronics and Communication Engineering Vol:1, No:10, 2007 1554 International Scholarly and Scientific Research & Innovation 1(10) 2007 scholar.waset.org/1307-6892/2851 International Science Index, Electronics and Communication Engineering Vol:1, No:10, 2007 waset.org/Publication/2851