Hankel approximation methods of IIR filter design

Presented in this paper are three design methods that use singular value decomposition and principal components analysis to construct IIR filters that approximate a desired filter response. The desired response may be specified in either the time domain or the frequency domain. The singular values of certain Hankel matrices constructed from the filter specifications, display the error in approximating the desired response by filters of different orders. The designer chooses the filter order based on the error that can be tolerated. An advantage common to these methods is that the user does not have to prespecify the filter order. Two of the new design methods have an additional advantage: They can be used when only the desired amplitude-response of the filter is specified, and the filter´s phase response is unimportant. (Finally, in comparison to some extant design methods, the methods investigated here, seem to produce high-quality filters using lower orders.)