Exploring the Evolutionary Bispectrum

Abstract

Since most of the natural phenomena have some characteristics varying with time, these types of phenomena or signals are classified as time-varying, or non-stationary signals. Therefore, dealing with these types of phenomena, like modeling or estimation, needs time-varying algorithms. For non-stationary processes, the conventional power spectrum does not reflect the time variation of the process characteristics. With the introduction of bispectrum in digital signal processing, a new approach to the solution of non-minimum phase system (NMP) identification problem is devised. This approach exploits the fact that the bispectrum contains information regarding both the phase and the magnitude of the system. Although bispectrum has been applied in identification of non-minimum phase LTI systems, it requires the assumption of stationarity and restricts the process to have non-symmetric probability density. When the input/output of the system are non-stationary, neither the power spectrum nor the bispectrum can handle this problem because they do not reflect the time variation of the process characteristics. In this paper, some algorithms based on the evolutionary spectrum to solve these problems are proposed. Our methodology to solve this problem is to use the theory of the evolutionary spectral and to introduce the evolutionary bispectral analysis. In this paper, a definition of the evolutionary bispectrum (EB) with its properties, especially the ability of removing non-stationary Gaussian noise, is discussed, and several algorithms for reconstructing the signal from the evolutionary bispectrum are also discussed.