# A matrix-based IRLS algorithm for the least \({l}_{p}\)-norm design of 2-D FIR filters

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## Abstract

Fast design of two-dimensional FIR filters in the least \({l}_{p}\)-norm sense is investigated in this brief. The design problem is first formulated in a matrix form and then solved by a matrix-based iterative reweighted least squares algorithm. The proposed algorithm includes two loops: one for updating the weighting function and the other for solving the weighted least squares (WLS) subproblems. These WLS subproblems are solved using an efficient matrix-based WLS algorithm, which is an iterative procedure with its initial iterative matrix being the solution matrix in the last iteration, resulting in a considerable CPU-time saving. Through analysis, the new algorithm is shown to have a lower complexity than existing methods. Three design examples are provided to illustrate the high computational efficiency and design precision of the proposed algorithm.

## Keywords

2-D FIR filter Least \(l_p\)-norm design Matrix-based algorithm Iterative reweighted least squares algorithm## References

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