Least-squares passband filters

The mathematical properties and design techniques of a novel low-pass filter type are described. A fifth-degree filter is designed, analyzed, and compared with its elliptic counterpart. This evaluation shows that the discrimination, phase, and delay properties of the two circuits are comparable; also, the time response of the proposed filter is substantially similar to that of an elliptic function filter. However, the loss responses are quite different: the loss of the least-squares filter is much less over the lower 90 percent of the passband. As a consequence, it is anticipated that the new circuit is best suited for the filtering of signals having most of their energies at lower frequencies.