Least mean square (LMS) error optimization is used to find the approximate FIR inverse of an FIR filter so as to make the overall filter coefficients closets to an impulse sequence. Then, a relation is sought between the LMS error and the z-plane zero positions of the FIR filter whose equal-length inverse is desired. Equations and boundaries showing regions where zeros should be confined in order not to exceed a specified error are given for filters of order two, four and multiples of four. © 1990.