The design of linear-phase low-pass filters

The general principles underlying the design of low-pass filters with quasi-linear phase characteristics are considered, and a method suitable for the design of certain low-pass filters required in television transmission equipment is described. Adequate linearity of phase response can be obtained over the whole pass band only by limiting the discrimination which is required in the attenuation region of the insertion-loss characteristic. If the phase linearity demands are relaxed at the lower part of the pass band of the low-pass filter, much higher discrimination can be obtained in the region above cut-off. These principles are illustrated by two examples. The first is a set of low-pass filters having linear phase characteristics from zero frequency to the region of cut-off frequency, with discriminations of 15 db or more above the transition interval. There are six independent filters in the set, having cut-off frequencies of 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 Mc/s. The second example is an asymmetric-sideband filter having a cut-off frequency of 6.12 Mc/s with an insertion-phase characteristic linear between 3 and 7 Mc/s; the discrimination exceeds 30 db above 7 Mc/s.