Design of adaptive envelope-constrained filters in the presence of impulsive noise

The problem of designing adaptive filters subject to output envelope constraints in the presence of impulsive noise at the input channel is investigated. Median smoothing is incorporated into the recently developed adaptive envelope-constrained filtering algorithms with a view to suppressing the effect of impulsive noise. It is demonstrated that the proposed adaptive filtering algorithms can provide notable improvements in the performance. In particular, the output envelope constraints of primary interest can be more easily satisfied by the filter weight estimate obtained with the median smoothing than with the average smoothing in impulsive noise situations. Numerical simulations are included to show the effectiveness of the proposed adaptive filtering algorithms.