A substantial part of Peranso's functions deal with the period analysis of astronomical data, also called time-series analysis. Although this  User Guide is not meant to be an introduction to period analysis, we want to spend a few words to present some background information about this topic.

A time-series is a series of observations (or measurements, data) taken at different times. E.g., the brightness estimates of a variable star form a time-series. We thus obtain a set of data pairs (ti, xi), where t is the time and x is the observation (data value). We assume that t is error free, and that x is a combination of the true signal, plus some error. 

Time-series analysis is the application of mathematics to quantify the variation of the data, i.e. we attempt to find some periodic behaviour in the data. Through this periodic behaviour, we ultimately want to learn something about the physics of the phenomenon represented by the sequence of observations. If we succeed to find a mathematical model that fits the observations, we may even try to predict the future behaviour of the system.

Time-series analysis isn't a field unique to astronomy, but it is used for many other applications, such as stock market analysis, economic forecasting, manufacturing engineering, and so on.

For an excellent introduction to time-series analysis in astronomy, presenting many useful examples, we refer to the book Analyzing Light Curves - A Practical Guide by Grant Foster. It seems to be out of print currently, but you will definitely find second hand copies on specialized websites. Further introductions are available on the AAVSO website and through some papers