1. A method of adaptive filtering for sparse system identification of an unknown system where the unknown system is sparse, comprising the steps of: tapping input signals to the unknown system; inputting the tapped input signals to a digital filter, the digital filter implementing a transfer function to produce corresponding output signals; tapping output signals of the unknown system corresponding to the input signals; summing the output signals of the unknown system with the inverse of the corresponding output signals of the digital filter to produce a feedback error signal; processing the feedback error signal with a least mean square algorithm having a variable step size computed according to: 
 μ( i +1)=αμ( i )+γ| e ( i )| where μ is the step size, α and γ are positive control parameters subject to 0<α<1, e is the estimation error, and i is an index correlating the input signal and output signals in order to recalculate coefficients of the transfer function; and updating the transfer function applied by the digital filter with the recalculated coefficients for application to the next succeeding input signal.