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A computational approach to the prediction of jet mixing noise is described. It is based on Lighthill's analogy, used together with a semi-deterministic modelling of turbulence (SDM), where only the large-scale coherent motion is evaluated. The features of SDM are briefly illustrated in the case of shear layers, showing that suitable descriptions of the mean flow and of the large-scale fluctuations are obtained. Aerodynamic calculations of two cold fully expanded plane jets at Mach numbers 0.50 and 1.33 are then carried out. The numerical implementation of Lighthill's analogy is described and different integral formulations are compared for the two jets. It is shown that the one expressed in a space–time conjugate (κ, ω)-plane is particularly convenient and allows a simple geometrical interpretation of the computations. Acoustic results obtained with this formulation are compared to relevant experimental data. It is concluded that the radiation of subsonic jets cannot be explained only by the contribution of the turbulent coherent motion. In this case, directivity effects are well recovered but the acoustic spectra are too narrow and limited to the low-frequency range. In contrast at Mach number 1.33, especially in the forward quadrant, results are satisfactory, showing that coherent structures indeed provide the main source of supersonic jet mixing noise.