System identification in the wavelet domain with crossband filters

In this paper, we present a wavelet domain system identification scheme, which takes into consideration the cross-terms between different frequency bands. Wavelet domain subband processing is advantageous whenever it produces a sparse representation of the processed signals. Perfect representation of linear time invariant (LTI) systems in the discrete-time wavelet transform (DTWT) domain requires time-invariant band-to-band filters and time-varying crossband filters between distinct subbands. We represent the response between two different subbands as a convolution with an appropriate multirate crossband filter. This reduces the model mismatch, which improves the identification in high SNR environment. The crossband filters formulation is extended to the two-dimensional wavelet domain. Experimental results demonstrate the advantages of crossband filters usage.