Comments on "Design of FIR Hilbert transformers and differentiators by eigenfilter
John W. Adams, G.W. Medlin · IEEE Transactions on Circuits and Systems · 1989
The authors of the above paper, S.-C. Pei and J.-J. Shyu, (ibid., vol.35, no.11, p.1457-61, Nov. 1988) claim that they obtain better performance than that of the McClellan-Parks algorithm. The commenters point out that, as the McClellan-Parks algorithm is mathematically optimal, it appears to be paradoxical that McClellan-Parks filters are claimed to be inferior to eigenfilters. The paradox is explained by noting that McClellan-Parks filters are optimal in the minimax sense and eigenfilters are optimal in the least-squares sense. It is concluded that when the performances of filters are compared, it is important to state the basis for comparison.>