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An algorithm and numerical code for the up-sampling of a system of particles, from a smaller to a larger number, is described. The method introduces a Poissonian `shot-noise' to the up-sampled distribution, typical of the noise statistics arising in a bunch of particles generated by a particle accelerator. The algorithm is applied to a 6-Dimensional phase-space distribution of relatively few simulation particles, representing an electron beam generated by particle accelerator modelling software, for subsequent injection into an Free Electron Laser (FEL) amplifier which is used here to describe the model. A much larger number of particles is usually required to model the FEL lasing process than is required to model the electron beam accelerators that drive it. FEL modelling software usually requires a much greater number of simulation particles than is required for modelling the acceleration stages and an increase in simulation particles is required while introducing the correct Poisson statistical properties of a real electron distribution. A numerical code developed from the algorithm was then used to generate electron bunches for injection into to an unaveraged 3D FEL simulation code, Puffin. Results show good qualitative and quantitative agreement with analytical theory. The program and user manual is available for download.