How to discover the caracteristic frequency of the use of an app by someone
I think a Fourier based frequency spectrum analysis may not be the best (most suitable) approach in providing you the necessary and useful information about that random service usage data. 

Instead I would suggest you to use statistical data analysis methods. These methods are the primary tools that are used to analyse user behaviour by collecting usage data and computing the resulting statistics upon them.

Creating the related random variables and estimating their associated probability density functions will allow you to formulate the average quantities such as the expected number of days (or hours) between two consequetive logins, expected day of week (or hour of day) of maximum usage, minimum usage etc, and therefore enable you to make optimizations of resource utilizations based upon them.