Wavelet-based transformations for nonlinear signal processing

Nonlinearities are often encountered in the analysis and processing of real -world signals, Ln this paper, we introduce two new structures for nonlinea r signal processing. The new structures simplify the analysis, design, and implementation of nonlinear filters and can be applied to obtain more relia ble estimates of higher order statistics. Both structures are based on a tw o-step decomposition consisting of a linear orthogonal signal expansion fol lowed by scalar polynomial transformations of the resulting signal coeffici ents, Most existing approaches to nonlinear signal processing characterize the nonlinearity in the time domain or frequency domain; in our framework a ny orthogonal signal expansion can be employed, In fact, there are good rea sons for characterizing nonlinearity using more general signal representati ons like the wavelet expansion. Wavelet expansions often provide very conci se signal representations and thereby can simplify subsequent nonlinear ana lysis and processing, Wavelets also enable local nonlinear analysis and pro cessing in both time and frequency, which can be advantageous in nonstation ary problems. Moreover, we show that the wavelet domain offers significant theoretical advantages over classical time or frequency domain approaches t o nonlinear signal analysis and processing.