Error reduction in computer-generated half-tone transparencies that are based on one-dimensional pulse-width modulation

The paper deals with the synthesis of band-limited functions that are generated by properly low-pass filtering 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 realised 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 half-tone transparencies is described