Error reduction in one-dimensional pulse-width modulation, with application to computer-generated transparencies

The paper deals with the synthesis of band-limited functions that are generated by the proper low-pass filtering of a sequence of equally spaced width-modulated unit-height pulses; simply choosing the pulse widths proportional to the corresponding sample values of the band-limited function to be generated would result in an error. The exact relationship between the pulse widths and the corresponding sample values of the band-limited function to be synthesized is derived. Error reduction can be achieved by using this relationship to calculate the pulse widths from the required sample values; in principle, a band-limited function can thus be realized to any degree of accuracy. It is shown which amount of error reduction can be obtained, when only a limited number of terms of the exact relationship is taken into account. The application to computer-generated halftone transparencies is described.