Comparison of the modified least squares and the weighted least squares algorithms for designing quadrature mirror filters

The least squares (LS) and the weighted least squares (WLS) algorithms are well known procedures that are used in the design of quadrature mirror filters (QMF). The equiripple nature of the WLS and its performance near the filter band edge has been reported to be better than that of the former. It is known that these design techniques suffer from a pass-band anomaly under certain conditions. Recently, it has been shown that the design anomaly in the LS algorithm can be overcome by using an initial guess filter obtained by a frequency sampling design (see Premkumar, A.B. and Vinod, A.P., IEEE Sig. Proc. Letters, vol.7, no.8, p.224-7, 2000). The same technique can be extended to overcome the pass-band anomaly in WLS filters. We present a comparison of modified LS and WLS designs based on simulation results. It is shown that the LS design is more robust, computationally less intensive and offers optimal performance over a wide range of cut-off frequencies.