In this paper, we propose a method for nonlinear system (NLS) identification using a swept-sine input signal and based on nonlinear convolution. The method uses a nonlinear model, namely, the nonparametric generalized polynomial Hammerstein model made of power series associated with linear filters. Simulation results show that the method identifies the nonlinear model of the system under test and estimates the linear filters of the unknown NLS. The method has also been tested on a real-world system: an audio limiter. Once the nonlinear model of the limiter is identified, a test signal can be regenerated to compare the outputs of both the real-world system and its nonlinear model. The results show good agreement between both model-based and real-world system outputs.

Exponential swept-sine signals are very often used to analyze nonlinear audio systems. A reexamination of this methodology shows that a synchronization procedure is necessary for the proper analysis of higher harmonics. An analytical expression of spectra of the swept-sine signal is derived and used in the deconvolution of the impulse response. Matlab code for generation of the synchronized swept-sine, deconvolution, and separation of the impulse responses is given. This report provides a...

In this paper, a method allowing the identification of two nonlinear systems in series is presented. More precisely, the identification of the second nonlinear subsystem under test is achieved by considering the effects of the nonlinearities of the first subsystem. The method is based on the estimation of the higher harmonic frequency responses from the measurement of distorted input and output signals. The second nonlinear system is then modeled by nonparametric generalized Hammerstein model made up of power series associated with linear filters. The method is experimentally validated in the well-known framework of nonlinear propagation of acoustic waves.

Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.

A new method of identification, based on an input synchronized exponential swept-sine signal, is used to analyze and synthesize nonlinear audio systems like overdrive pedals for guitar. Two different pedals are studied; the first one exhibiting a strong influence of the input signal level on its input/output law and the second one exhibiting a weak influence of this input signal level. The Synchronized Swept Sine method leads to a Generalized Polynomial Hammerstein model equivalent to the pedals under test. The behaviors of both pedals are illustrated through model-based resynthesized signals. Moreover, it is also shown that this method leads to a criterion allowing the classification of the nonlinear systems under test, according to the influence of the input signal levels on their input/output law.