Short-time signal representation by nonlinear difference equations

Methods are investigated for short-time analysis and synthesis of signals from a class of second-order difference equations with a cubic nonlinearity. In analysis, two methods are explored for estimating equation coefficients: (1) prediction error minimization (a linear estimation problem) and (2) waveform error minimization (a nonlinear estimation problem). In the latter case, which improves on the prediction error solution, an iterative analysis-by-synthesis method is derived which allows as free variables initial conditions, as well as equation coefficients. Parameter estimates from these techniques are used in sequential short-time synthesis procedures. Possible application to modeling quasi-periodic behavior in speech waveforms is discussed