This article presents the development of a neutron noise calculation technique with a reduced calculation time based on the TFM (Transient Fission Matrix) approach. The latter contains different information such as the system transfer function (fission and absorption probability density functions and corresponding neutron multiplicity) of prompt and delayed neutrons, and the corresponding propagation time. This information is used to reconstruct neutron showers based on precursor decays up to the shower disappearance by absorption, leakage or delayed neutron precursor creation. Then pseudo-detectors such as fission chamber count rate histograms are reconstructed from these neutron showers and the α_prompt is calculated from the cross-correlation function. A very good agreement has been obtained on the uranium-fueled light water reactor CROCUS between the model developed and the reference value.