The noise production by ducted single- and double-diaphragm configurations is simulated using a stochastic noise generation and radiation numerical method. The importance of modeling correctly the anisotropy and temporal de-correlation is discussed, based on numerical results obtained by large eddy simulation. A new temporal filter is proposed, designed to provide the targeted spectral decay of energy in an Eulerian reference frame. An anisotropy correction is implemented using a non-linear model. The acoustic propagation problem is solved using Lighthill's aeroacoustic analogy with a tailored Green's function obtained analytically. Comparison with scale-resolved data indicates that accurate far-field noise predictions are obtained for both single and double diaphragm configurations, with computational costs significantly reduced with respect to the scale-resolved approach. A grouping scheme for the noise sources based on the octree structure is introduced to minimize the memory requirements and further reduce the computational cost.