Wavelet Transforms for Nonlinear Signal

Robert Nowak Michigan State University East Lansing, MI 48824-1226 Email: [email protected] WWW: http://www.egr.msu.edu/spc/ Richard Baraniuk Rice University Houston, TX 77251-1892 Email: [email protected] WWW:http://www-dsp.rice.edu ABSTRACT In this paper we describe two new structures for nonlinear signal processing. The new structures simplify the analysis, design, and implementation of nonlinear lters and can be applied to obtain more reliable estimates of higher-order statistics. Both structures are based on a two-step decomposition consisting of a linear orthogonal signal expansion followed by scalar polynomial transformations of the resulting signal coe cients. While most existing approaches to nonlinear signal processing characterize the nonlinearity in the time domain or frequency domain; in our framework any orthogonal signal expansion can be employed. In fact, there are good reasons for characterizing nonlinearity using more general signal representations like the wavelet transform. Wavelet expansions often provide very concise signal representation and thereby can simplify subsequent nonlinear analysis and processing. Moreover, we show that the wavelet domain o ers signi cant theoretical advantages over classical time or frequency domain approaches to nonlinear signal analysis and processing.