Mysore R. Raghuveer

Bispectrum estimation via AR modeling

Abstract The bispectrum of process is a quantity that provides information about quadratic phase coupling of its harminic components and also deviation from normality. This information is essentially contained in its third moment sequence. In this paper a new method that provides a bispectrum estimate in terms of the frequency response of an autoregressive (AR) filter is presented. The parameters of the filter try to approximate the third moments of the underlying process. This method is shown to provide much higher resolution than existing conventional methods for bispectrum estimation and is especially suitable for short length data.

A parametric approach to bispectrum estimation

Higher order spectra provide information about processes not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality. The bispectrum which is a third order spectrum provides information about quadratic phase coupling among harmonic components. Bispectrum estimation has been applied in diverse fields principally to obtain such information. Existing methods for bispectrum estimation are patterned after the conventional methods for power spectrum estimation which are known to possess certain limitations. The paper proposes a parametric approach to bispectrum estimation based on AR modeling of time series. The definition and properties of a parametric bispectrum estimator in the general ARMA case are stated. The third moment recursion equations that follow from the model assumptions for the proposed AR bispectrum estimator are presented. The estimates are derived using biased estimates of the third moments in these equations. Results from preliminary experiments suggest that the resulting method does possess certain attractive features when compared with existing methods.

A new class of high-resolution and robust multi-dimensional spectral estimation algorithms

A new class of multi-dimensional (m-D,m=3,4) spectral estimation algorithms is introduced based on the minimum variance representations (MVR) of m-D (m=3,4) data fields. These representations are defined in the framework of linear prediction where it is shown that they may be classed into general categories depending upon the geometry of the prediction space. For example, in the 3-D case it is shown that there are four possible models: causal, semicausal I, semicausal II, and non-causal. The m-D (m=3,4) model formalisms and their linear-predictive and spectral interpretations are derived. The admissibility conditions of the spectral density function are also discussed. To obtain high-resolution spectral estimates from finite length m-D (m=3,4) data fields, the models are fitted to the data optimally in the sense of minimizing the covariance recursion errors within the prediction space considered. Computer-simulated short data fields consisting of two travelling waves embedded in noise are employed to demonstrate experimentally that the class of algorithms developed in this paper improves on the standard techniques for high-resolution and robustness in the presence of nonstationarities, such as envelope modulation.

Digital image halftoning by noise thresholding

Approaches for digital halftoning of images using dithering threshold the input image with additive dithering noise. The paper presents a technique which thresholds the noise directly. The threshold is modified at each step such that the expected value of the output is equal to the input pixels gray value. Further, error feedback is used to correct the threshold. Tests on images show the methods ability to retain features in the high frequency regions such as edges as well as low frequency features such as slow variations in intensity. One advantage the proposed method is its very general nature since it offers a wide choice of the three filters: noise shaping filter, feedforward filter and feedback filter.