PSR J0337+1715 is a millisecond radio pulsar in a hierarchical stellar triple system with two white dwarfs. This system is a unique and excellent laboratory in which to test the strong equivalence principle (SEP) of general relativity. An initial SEP-violation test was performed using direct 3-body numerical integration of the orbit in order to model the more than 25000 pulse times of arrival (TOAs) from three radio telescopes: Arecibo, Green Bank and Westerbork. In this work I present our efforts to quantify the effects of systematics in the TOAs and timing residuals, which limit the precision of an SEP test. In particular, we apply Fourier-based techniques to the timing residuals in order to isolate the effects of systematics that can masquerade as an SEP violation.