OPTIMUM FIR FILTER FOR SAMPLED SIGNALS IN PRESENCE OF JITTER

Abstract The requirements of the integrated readout electronics for calorimetry at high luminosity hadron colliders pose new challenges both to hardware design and to the performance of signal processing algorithms. Both aspects have been treated in detail by the FERMI(RD16) 1 collaboration [C. Alippi et al., Nucl. Instr. and Meth. A 344 (1994) 180], from which this work has been motivated. The estimation of the amplitude of sampled signals is usually performed with a digital FIR filter, or with a more sophisticated non linear digital filter using FIR filters as building blocks [S.J. Inkinen and J. Niittylahti, Trainable FIR-order statistic hybrid filters, to be published in IEEE Trans. Circuits and Systems; H. Alexanian et al., FERMI Collaboration, Optimized digital feature extraction in the FERMI microsystem Nucl. Instr. and Meth. A 357 (1995)]. In presence of significant signal phase jitter with respect to the clock, the phase dependence of the filter output can be a major source of error. This is especially true for measurements of large amplitudes for which the effect of electronic noise becomes negligible. This paper reports on the determination of digital FIR filters that optimize the signal over noise ratio due to known jitter distributions for different filter lengths. As the presence of electronic noise is neglected, the results are mainly relevant for measurements of large signals.