Region-Based Wavelet-Packet Adaptive Algorithm for Identification of Sparse Impulse Responses

Identification of systems with sparse impulse response encounters large applicability. Numerous techniques have been proposed to identify such systems efficiently. One strategy that leads to specially good results is to detect the active (nonzero) response samples and update only the corresponding adaptive coefficients. Wavelet-based approaches have been shown to be specially effective to this end. This paper proposes a new region-based wavelet-packet (RBWP) algorithm for efficient identification of systems with sparse impulse responses with arbitrary frequency spectra and with any delay of the effective response. The discrete wavelet packet transform (DWPT) is adaptively tailored to the energy distribution of the unknown system´s response spectrum. The new algorithm leads to a reduced number of active weights and to a reduced computational complexity, when compared with competing wavelet-based algorithms. Monte Carlo simulation results show good performances regarding convergence speed and robustness to design parameter choice.