An Iterative Technique for Determining Inverse Filters

It is the objective of much geophysical research to increase the resolution of signals recorded on a sluggish measuring device. The approach genreally followed is to use inverse digital filters. This treatment presents an iterative technique for obtaining "stable inverse digital filters." A stable inverse filter is one whose impulse response decays to zero with increasing time. An optimum inverse filter R(¿) is defined here as R(¿)=1/H(¿), where H(¿)¿0; R(¿)=0, where H(¿)=0. It is shown that one can converge to this solution by operating in the time domain using the method of successive substitution. This approach to inverse filtering is unique in that the inverse filter is obtained by an iterative technique, thereby eliminating the dependence on computer limitations, as indicated in some reported techniques. In addition, a method of handling the zero crossings of H(¿) is posed. A smoothing technique to modify these filters for inverse filtering in the presence of noise is also presented.