The distinguishing characteristic of the Hourglass filter is that the reflection zero frequencies are exactly the inverse of the transmission zero frequencies. The Hourglass filter is similar to the Chebyshev Type II Filter, but has a sharper cut-off, a higher group delay, and greater stop band attenuation. The passband also contains a slight equiripple characteristic which makes the Hourglass a special case of the Elliptic filter.
Like the Chebyshev Type II Filter, the passband attenuation of the Hourglass Filter is defined to be -3.01 dB. However, FilterSolutions allows the user the option of selecting any passband attenuation (in dB) that will define the filters cut off frequency. The Hourglass flter was first derived by Dr. Byron Bennett of Montana State University, and is documented in IEEE Transactions on Circuits and Systems. (December 1988; vol. 12; p. 1469).
Shown below are examples of 5th order Hourglass low-pass, high-pass, bandpass and bandstop filters and low-pass step response. The stop-band ratio is 1.2 in all cases.
It is useful to compare the stop-band attenuation and the group delay to that of the Chebyshev II and Elliptic Filters.