Large-Eddy Simulation (LES) is a powerful formulation for model turbulent reacting flows that balances lower resolution with predictions of variance dominant momentum and energy fluctuations. LES assumes that energy-dominated turbulence motions are resolved scale (RS) and forward cascade-dominant, so that modeled effects of sub-filter scale (SFS) motions are higher order. However, the application of this scale-based decomposition to reacting turbulent flows is problematic since dynamically important kinetics within thin flame regions are mostly SFS. Our aim here is systematic refined kinematics analysis of the relationships between coherent structure in physical and scale space relevant to LES of premixed turbulent combustion. We begin with reduced physics simulations of the interactions between single-scale vortex arrays and laminar premixed flames. To characterize physical-space/scale-space relationships, we apply the Fourier description using a newly developed procedure to remove spurious Fourier spectral content associated with boundary discontinuities in the non-periodic directions of bounded signals. Using Fourier-space filters, we identify characteristic coherent structural features concurrently in physical and Fourier space in response to flame-eddy interactions and their relative contributions to the SFS and RS variance content of the primary variables of interest (momentum, energy and species mass concentration). The primary variables within the dynamical system were classified based on RS vs. SFS variance content, and distinct structural features in physical and Fourier space were identified for each class. We show that the SFS variance for all variables analyzed is associated with the SFS corrugated flame front, which in 2D Fourier space is associated with a coherent broadband “star-like” pattern that extends from the resolved to the flame subfilter scales. The directional dependences, magnitudes and phase relationships among the Fourier coefficients within the “legs” of the star reflect the power-law spectral representation of fronts and are shown to be closely connected with the direction and magnitude of flame-normal gradients of key variables within the corrugated flame front. This work provides a deeper understanding of the relationships between coherent structural features of flame-turbulence interactions in physical space and Fourier space as a key step in the determination of dominant dynamical impacts of SFS content and the evolution of RS variables in LES of premixed turbulent combustion.