Estimating sampling frequency offset
As mentioned in a comment, what you describe looks like a timing recovery algorithm for digital communications.
I can recommend two sources, an article and a chapter in a book, which give a nice introduction and overview of the topic in general:

L. R. Litwin, «Matched filtering and timing recovery in digital receivers», RF Design, pp. 32–48, Sep. 2001.

M. Rice, «Chapter 8. Symbol Timing Synchronization», in Digital Communications: a Discrete-Time Approach, Upper Saddle River, N.J: Pearson/Prentice Hall, 2009.