Inverse filtering for systems with unit circle zeroes

This paper discusses the problem of reducing distortion introduced by a known distorting filter G. The distorting filter has a symmetric unit pulse response so that no phase distortion is introduced. However the example presented in this paper involves a filter with several unit circle zeroes. These frequency domain zeroes rule out inverse filtering techniques which amount to choosing a compensation filter H(ω) with H(ω) = 1/G(ω). The problem described here arises in well logging where the system performance is evaluated in terms of step inputs. Chebychev approximation techniques are applied to find an FIR compensator so that the compensated step response has the minimum possible overshoot for a given rise time.