Analisi e progettazione di filtri IIR derivativi per segnali quantizzati. Analysis and design of IIR differentiator for quantized signals

The IIR differentiators are nowadays largely studied for different kind of uses, such as in Sigma-Delta modulation and data compression. However, estimation of velocity, based on quantized signals (i.e. provided by incremental optical encoder) and using differentiators is still a challenge, since the quantization process has an associated error that shows non-linearity properties. The thesis provides a complete framework on IIR digital differentiators when used for velocity estimation with quantized position signals as input: the most important is a procedure that allows everyone to calculate the mean square error at the output of the filter when the autocorrelation of the input error is known. This achievement can be also applied to every kind of IIR filter giving to it a wide range of applications. Moreover, a comparison between the real error and the white noise approximation has been made, and also a new approximation, based on the worst case, has been developed. Last, a full spectral analysis of the filters and signals has been provided. Most of the results above have been provided and tested for the constant rate case, in order to optimize the IIR differentiator for system with low frequencies rate of change