Identification of sparse impulse responses - design and implementation using the partial Haar block wavelet transform

This paper proposes an implementation for identifying sparse impulse responses. The new scheme follows the approach in which the location of the channel response peak is estimated in the wavelet domain. A short time-domain adaptive filter is then located about the estimated peak to identify the sparse response. The primary purpose of this paper is to present an efficient design of such a system. The use of a new block wavelet transform results in up to 70% less computational complexity and improved peak detection, as compared to previous solutions. A new robust time-domain adaptive filtering location and update scheme is also proposed that significantly reduces the occurrence of jitter problems and leads to improved residual mean-square error performance. The behavior of the transform-domain adaptive filter is analyzed, the Wiener solution is determined, and an accurate analytical model is obtained for the mean-square deviation of the adaptive coefficients. Monte Carlo simulations show excellent echo cancellation performance for typical ITU-T echo channels.