A new filter synthesis technique-the hourglass

A synthesis procedure called the hourglass algorithm is discussed. This algorithm produced filters that have better passband and stopband characteristics than conventional maximally flat filters. It is argued that its use throughout filter design unifies, simplifies, and systematizes synthesis procedures. The improvement in the passband achieved by the hourglass over the maximally-flat filter is due to the distribution of reflection coefficient zeros throughout the passband. The improvement in the stopband occurs because the natural modes of the hourglass are nearer the passband and farther from the stopband than the corresponding maximally-flat natural modes. These conditions are the result of reciprocal location of the reflection coefficient zeros with respect to the transmission zeros. The technique yields filters comparable to the classical constant-k filters with m-derived end sections. As opposed to the classical filters, the specified magnitude at the band edge may be realized exactly. Simple transformation of the zeros of hourglass designs leads to standard Chebyshev, Chebyshev rational fraction, and elliptic (Cauer) designs. Several filter design examples are provided to illustrate the method.>