The adaptive filter for sparse system identification is an adaptive filter that uses an algorithm in the feedback loop that is designed to provide better performance when the unknown system model is sparse, i.e., when the filter has only a few non-zero coefficients, such as digital TV transmission channels and echo paths. The algorithm is a least mean square algorithm with filter coefficients updated at each iteration, as well as a step size that is also updated at each iteration. The adaptive filter may be implemented on a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or by field-programmable gate arrays (FPGAs).