Summary: 1326 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS--I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 48, NO. 11, NOVEMBER 2001
Novel Stable Higher Order -to- Transforms
Mohamad Adnan Al-Alaoui
Abstract--Novel stable higher order -to- transforms are introduced.
A class of second-order stable transforms is obtained by stabilizing the class
of second-order integrators resulting from interpolating the Simpson and
the trapezoidal rules. In addition new transforms are obtained by stabi-
lizing the -to- mapping functions obtained from the AdamsMoulton
numerical integration formulas. The approach is general and can be ap-
plied to other integration rules to obtain stable transforms. An important
advantage of the new stabilized rules is that they yield minimum phase fil-
ters when applied to analog all-pole filters.
Index Terms--Differentiators, digital filters, digital signal processing, in-
tegrators, -to- transforms, Simpson rule, trapezoidal rule.
First-order numerical integration, or differentiation rules are often
employed to obtain s-to-z transformations. The most famous of the
numerical integration-based mappings are the bilinear (Tustin) trans-
formation, obtained from the trapezoidal integration rule, and the back-