Transform domain second-order nonlinear Wiener adaptive filtering for colored Gaussian signals

Presents the concept of transform-domain (TD) adaptive filtering based on the discrete nonlinear Wiener model for a 2nd-order Volterra system identification application with a colored Gaussian input signal. In earlier work (1999), we presented the 2nd- and 3rd-order nonlinear discrete Wiener adaptive algorithm, and its performance analysis focused on the Gaussian white input case. In this paper, we present new results for the colored Gaussian input environment. From the analysis, we realize that the nonlinear Wiener model has many advantages over other models, such as the Volterra model. The main advantage is that, for both white and colored Gaussian input, it can have a reasonably fast convergence speed and low computational complexity. This is because the nonlinear Wiener model performs a complete orthogonalization procedure to the truncated Volterra series which allows us to use linear adaptive filtering algorithms to calculate all the coefficients efficiently. For a Gaussian colored input signal, the TD nonlinear Wiener model is introduced to decouple the colored effect. Computer simulation results of discrete cosine transform (DCT) domain nonlinear Wiener adaptive filtering with 1st-order autoregressive colored Gaussian input are presented to verify the theoretical analysis.