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.