Representation and Identification of Nonlinear Systems in the Short-Time Fourier Transform Domain

In this chapter, we introduce a novel approach for improved nonlinear system identification in the short-time Fourier transform (STFT) domain. We first derive explicit representations of discrete-time Volterra filters in the STFT domain. Based on these representations, approximate nonlinear STFT models, which consist of parallel combinations of linear and nonlinear components, are developed. The linear components are represented by crossband filters between subbands, while the nonlinear components are modeled by multiplicative cross-terms. We consider the identification of quadratically nonlinear systems and introduce batch and adaptive schemes for estimating the model parameters. Explicit expressions for the obtainable mean-square error (mse) in subbands are derived for both schemes. We show that estimation of the nonlinear component improves the mse only for high signalto- noise ratio (SNR) conditions and long input signals. Furthermore, a significant reduction in computational cost as well as substantial improvement in estimation accuracy can be achieved over a time-domain Volterra model, particularly when long-memory systems are considered. Experimental results validate the theoretical derivations and demonstrate the effectiveness of the proposed approach.