To enable the later determination of nearly optimum, realizable position decoding filters for position sensitive detectors as well as to enable valid comparisons of various position sensitive detectors, we introduce in this work a productive, high‐quality approximation to the point‐spread function for position sensitive detectors that use pulse‐shape modulation and crossover‐time demodulation. This approximation is the result of a theoretical calculation and is determined as a general function of the input signal and rms noise at the input to each of the two crossover detectors. It is precisely applicable to position sensitive detectors that use any type of transmission line encoding. The effects of random variables, such as charge collection time, are included in the calculation, but the effects of correlated noise in the two channels are not included. In addition, for the broad class of position sensitive detectors that have electronic and thermal noise as the dominant causes of position uncertainty, general equations, based on our approximate point‐spread function, are given for the optimum filter impulse responses, the optimum pulse shapes at the inputs to the crossover detectors, and the associated minimum positional full‐width half‐maximum (FWHM). General equations are also given for positional FWHM of electronic‐noise‐limited detectors that use nonoptimum filters. Finally, for electronic‐noise‐limited detectors that use an RC‐transmission line encoder that is terminated in its characteristic impedance, a plot is given of the optimum pulse shape at the input to the crossover detectors.