LAUSR

Optimization problem formulation for semi-digital FIR digital-to-analog converter (SDFIR DAC) is investigated in this work. Magnitude and energy metrics with variable coefficient precision are defined for cascaded digital $$\varSigma \varDelta$$ΣΔ modulators, semi-digital FIR filter, and Sinc roll-off frequency response of the DAC. A set of analog metrics as hardware cost is also defined to be included in SDFIR DAC optimization problem formulation. It is shown in this work, that hardware cost of the SDFIR DAC, can be significantly reduced by introducing flexible coefficient precision while the SDFIR DAC is not over designed either. Different use-cases are selected to demonstrate the optimization problem formulations. A combination of magnitude metric, energy metric, coefficient precision and analog metrics are used in different use cases of optimization problem formulation and solved to find out the optimum set of analog FIR taps. A new method with introducing the variable coefficient precision in optimization procedure was proposed to avoid non-convex optimization problems. It was shown that up to 22% in the total number of unit elements of the SDFIR filter can be saved when targeting the analog metric as the optimization objective subject to magnitude constraint in pass-band and stop-band.