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Recently, sparse signal approximation has become an increasingly important research area in signal processing. It attracts a lot of interest due to its wide range of practical applications. In this work, a novel adaptive filtering algorithm with relative low computational complexity that is capable of exploiting the sparsity of systems is proposed. The basic idea here is, we adopt a p-norm constraint in the cost function of the variable step-size least mean square (VSSLMS) algorithm. This constrain imposes a zero attraction at each filter coefficient based on their respective relative value....