Comparison between Digital Filters and Singular Value Decomposition to Reduce Noise in LHC Orbits used for Action and Phase Jump Analysis

One of the initial difficulties to apply the Action and Phase Jump (APJ) analysis to LHC orbits was the high level of noise present in the BPM measurements. On the other hand, the unprecedented number of turns for LHC allows us to use all sort of filters. In this paper, we evaluate the effectiveness of digital filters like the band-pass filter and compare them with a filter based on Singular Value Decomposition, when magnetic error estimations are made using a recent version of the APJ method. First, mainly results on simulated orbits with noise are presented, and then, plots and results are shown for the filters effect on experimental data. The analysis indicates that a combination of filters leads to measurements with the least uncertainty.