Time-domain and Frequency-domain Signals and their Analysis

TL;DR

This paper explores the mathematical foundations and practical applications of analyzing signals in both time and frequency domains, focusing on accelerator measurements including single, periodic, and multi-bunch signals.

Contribution

It provides a comprehensive overview of signal analysis techniques tailored to accelerator physics, integrating theoretical background with real measurement examples.

Findings

Effective analysis of signals in accelerator measurements.

Comparison of time-domain and frequency-domain methods.

Application to various accelerator signal types.

Abstract

Depending on the application people use time-domain or frequency-domain signals in order to measure or describe processes. First we will look at the definition of these terms, produce some mathematical background and then apply the tools to measurements made in the accelerator domain. We will first look at signals produced by a single bunch passing once through a detector (transfer line, linac), then periodic single bunch passages (circular accelerator) and at the end multi-bunch passages in a circular accelerator.