Journal of VLSI Signal Processing 45, 21–28, 2006 * 2006 Springer Science + Business Media, LLC. Manufactured in The Netherlands. DOI: 10.1007/s11265-006-9769-2 Effective Parametric Estimation of Non-Gaussian Autoregressive Moving Average Processes Exhibiting Noise with Impulses PRESTON D. FRAZIER General Dynamics Corporation, 1340 Ashton Road, Hanover, MD 21076, USA M. F. CHOUIKHA Department of Electrical and Computer Engineering, Howard University, Washington, DC 20059, USA Received: 21 March 2005; Revised: 29 May 2005; Accepted: 6 June 2005 Abstract. In statistical signal processing, parametric modeling of non-Gaussian processes experiencing noise interference is a very important research topic. Particularly challenging to some researchers is how to estimate signals encountering stochastic noise process exhibiting sharp spikes. The authors propose the use of systems with impulse effect along with the classic autoregressive moving average model as a novel parametric modeling tool to successfully estimate these specific processes. The proficiency of this original system is illustrated in a performance table. Keywords: non-Gaussian processes, impulse effect, autoregressive moving average models, stochastic noise 1. Introduction Efficient estimation of parameters of stochastic processes is an important topic in signal processing. The use of time series models, such as autoregressive (AR), moving average (MA), and in particular autoregressive moving average (ARMA), are very effective techniques to model the parameters of non- Gaussian systems [1–8]. The use of ARMA system identification has been applied in several areas, such as adaptive filtering [9], seismic data processing [10], and communication systems [11]. The ARMA models have been shown to be sufficient methods for estimating parameters of non-Gaussian systems. However, the main caveat in the analysis of these processes is that the additive noise is Gaussian. Given this requirement, the most appealing method to elucidate these signals is to use higher-order statistics (HOS), also known as cumu- lants [5, 7, 10]. The motivation behind the use of HOS is that they are phase blind to all kinds of Gaussian noise. Hence, if a signal is non-Gaussian and the additive noise is Gaussian, then the noise will vanish when elucidat- ing within the cumulant domain. The reason is HOS are insensitive to any type of Gaussian noise because HOS for normal processes are identically zero [7]. However for many applications, modeling the noise as a Gaussian process is not appropriate. Many noise processes studied are non-Gaussian. Some physical phenomena generate stochastic noise with sharp spikes (ergo impulses). There are innate, as well as manufactured, sources of spike interference which exist, including atmospheric noise, which degrades low frequency communication systems [12], switch- ing transients in telephone lines [13], acoustic emission signals, and ice cracking in the arctic region [14]. The popular Gaussian model is not flexible enough to incorporate these swift, significant amplitude-varying impulses mainly because of the