Optimal multibit Digital to Analog Conversion

When employing multibit data converters the necessity arises to compensate for digital to analog converter (DAC) element mismatch. The most widespread compensation techniques are based on digital element matching (DEM) and, if properly designed, these can achieve almost arbitrary DAC mismatch noise shaping. This paper gives a closed form expression for the optimal DEM noise shaping profile. It depends upon the spectrum of the analog signal to be quantized and may also include a frequency weighting filter which reflects perceptual criteria.