• beam instrumentation
• accelerator physics
• digital signal processing
• sampling theory
• direct digitisation

With the technology improvements of Analog-to-Digital Converters (ADC), notable in terms of sampling rate and resolution, the direct digitisation of beam pickup signals is of growing interest in the field of particle beam diagnostics for charged particle accelerators.
This thesis studies the possibility to acquire and measure the transverse position of a charged particle beam in an accelerator, using an architecture based on minimum analogue signal conditioning of the Beam Position Monitor (BPM) signals, direct digital conversion, and measurement of the power of each beam bunch-related pulse signal in the digital domain. The aim is to analyse the impact of the characteristics of the sampling stage on the system resolution performance.
The effects of the distortion due to the sampling process, and of the finite resolution of the ADC, are discussed analytically in detail. They are expressed in form of a general, analytic expression of the signal-to-noise ratio of the measurement for any pulse waveform as function of the characteristics of the ADC.
The presented model was applied to analyse the performance of the Large Hadron Collider beam extraction interlock BPM system, an example of system implementing direct-digitisation of BPM signals. A prototype setup was used to acquire beam data with two different ADCs. The system was also replicated in a parametric simulation framework and the estimated performance from analytical prediction, simulation, and measurements are compared.