Motivated by the challenges of learning interpretable dynamic models from noisy experimental observations, in this talk we explore the problem of test function design and selection in weak form system identification for systems of ODEs. Weak form methods such as Weak SINDy have emerged as promising and robust approaches for recovering parsimonious models from data corrupted by noise. However, performance of these methods is heavily contingent on the selection of a good test function basis. For this reason, significant effort in recent literature has been devoted to the problem of data-driven test function construction, with most works focused on optimizing parameters in piecewise polynomial or Gaussian bump functions to enforce a compact support condition. In this talk, taking inspiration from classical Modulating Function Methods for system identification in the systems and control literature, we relax the compact support constraint and illustrate that a simple choice of sinusoidal test functions presents significant advantages over the more widely utilized constructions. Firstly, under this problem setup, the identification problem reduces to a simple regression over Fourier series coefficients that are efficiently computable with FFT. Secondly, the data-driven test function selection problem reduces to a classical spectral density estimation problem. We illustrate efficacy and robustness of this approach on a variety of chaotic benchmark systems and discuss future directions.