Bandpass and bandstop recursive filters with low sensitivity

In a sharp cutoff bandpass or bandstop recursive digital filter, the poles and zeros are expected to be clustered around the band edges, and in close proximity of the unit circle in the z-plane. Implementation of such filters with low sensitivity could be achieved by cascading second-order sections, with appropriate low sensitivity structures chosen for individual sections depending on the locations of the poles. An alternative approach for design and implementation of band-pass/bandstop filter with low sensitivity is shown to be based on transformation of sensitivity characteristics of a low sensitivity structure to appropriate angular regions on the unit circle. A fourth-order section of such a filter is realized with a level of sensitivity which is the same as that of the prototype second-order low-pass filter section realized with low sensitivity and with reduced number of multiplications. A few transformations along with their respective structures for transforming a prototype low-pass filter are given.