This reminds me a bit of Fourier transformations from time- to frequency-domain. Where an arbitrarily complex time-series signal can be accurately represented

This reminds me a bit of Fourier transformations from time- to frequency-domain. Where an arbitrarily complex time-series signal can be accurately represented as the sum of various sine waves. Except the OP deals with a discretized values, not real-number values, and the OP's approach lets the constituent palindromes start/end at an arbitrary offset, rather than having to be repeated continuously.