To provide a quantitative assessment of the source-receptor relationship in an Eulerian framework, the method of artificially adding oscillatory signals with different frequencies to emission locations for a scalar is evaluated. Two-dimensional numerical experiments of nonlinear hydrostatic mountain waves with wave breaking were used. The scalar time series were collected at a number of downstream locations and decomposed into frequency space to identify their sources and to investigate the strength of those signals with respect to different diffusion schemes. Six experiments were conducted using three sub-grid eddy coefficients (a constant, a function of deformation, and a function of turbulence kinetic energy (TKE)) and two environmental wind conditions (shear and no shear). Simulated oscillatory signals were affected by parameterized sub-grid-scale diffusions. Signals experiencing more sophisticated eddy coefficients were better preserved than those with the simplest constant ones. The signals were shifted to higher frequencies when using the TKE scheme under a uniform wind environment.