Squared amplitude frequency response and Chebyshev techniques applied to continued fraction transfer-function approximates

Abstract

A continued fraction (Pade) approximant is discussed, based on the ‘ amplitude-squared frequency response ’ of the original system. A study is also made of modifications to the Pade approximant, due to Maehly, based on Chebyshev rather than Maclaurin series. By introducing the concept of ‘ shifting ’ allied to the amplitude-squared technique, the reduced model can be made an approximant over a specified range of frequencies, including band-pass systems. It is concluded that these techniques offer some interesting extensions to the continued fraction model reduction methods but fail to provide the all-purpose solution sought after ; the Chebyshev techniques, already established in numerical analysis, are not so successful in model reduction.