1. An adaptive filter for sparse system identification of an unknown system, comprising: a digital filter having an input for receiving successive input signals and an output for outputting corresponding output signals according to a transfer function, the input signals also being input to an unknown sparse system, the unknown sparse system producing corresponding reference signals; an inverter connected to the digital filter, the inverter being configured to invert the output signals of the digital filter; a summer connected to the inverter, the summer receiving the reference signals and the inverted output signals, the summer being configured for summing the reference signals and the inverted output signals to produce corresponding error signals; an algorithm unit connected to the summer, the algorithm unit being configured to receive the error signal and having means for recalculating coefficients of the transfer function to adjust for the error signal, the means for recalculating implementing a least mean square algorithm and having means for adjusting a step size of the least mean square algorithm 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; and an updater unit connected to the algorithm unit, the updater unit updating the transfer function applied by the digital filter with the recalculated coefficients from the algorithm unit for application to the next succeeding input signal; whereby the adaptive filter's output signals initially converge rapidly to the unknown sparse system's reference signals, and then converge more slowly to correlate more closely with the unknown system's reference signals.