The testing of analog-digital converters (ADC's) is an important task in the industry. The testing is necessary to prove that the converter meets the specifications. It is important for the manufacturer to ensure every product it sells conforms to the specifications. Testing is equaly important for the user, because the whole circuit may fail, if it contains a faulty converter.
The IEEE 1241-2010 standard contains the specifications of A/D converters as well as the measurement setup. The most important method is based on sine fitting: a pure sine wave is connected to the input and the parameters of the wave are fitted to the output code with least-squares method. Some of the errors of the converter can be calculated from the difference of the output and the fitted signal. The estimation of the errors depends on the accuracy of the sine fitting method.
According to the estimation theory, for known comparison levels and for Gaussian input noise there is a better fitting method than least squares: the maximum likelihood method. I coded the maximum likelihood method, and compared it to the least squares method using simulations.