Lp-complex approximation using iterative reweighted least squares for FIR digital filters

This paper examines the use of the iteratively reweighted least squares (IRLS) error algorithm to obtain an L_p-approximation for the design of FIR digital filters with a complex-valued desired frequency response. The algorithm presented, introduced by Burrus and Barreto (see IEEE Proceed. ISCAS 92, p.545, 1992) for the design of 1-D linear-phase FIR filters, considers the case of 2<p<∞ and is useful in the design of filters that give a trade-off between the traditional L₂ and L_∞ designs. The algorithm proposed deals directly with the complex error function and performs better than the extended Lawson algorithm. An important feature of the method is that does not require knowledge of the location of the extremal points as it is the case for single or multiple exchange algorithms. Convergence of the new algorithm is discussed and several filter examples are presented