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The automation of fixed-point conversion requires fast methods to evaluate the numerical accuracy of the system. As an alternative to a simulation-based approach, most of the analytical methods use perturbation theory to provide the expression of the quantization noise at the output of a system. Most existing analytical methods do not consider a correlation between noise sources. This assumption is no longer valid when a unique datum is quantized several times. This brief proposes to study the correlation between quantization noises with different quantization modes (truncation and rounding) and considering the number of eliminated bits. Then, the expression of the power of the output quantization noise is provided when the correlation between the noise sources is considered. The proposed approach allows improving significantly the estimation of the output quantization noise power compared to the classical approach, with a slight increase of the computation time. In our experiment, the maximal relative estimation error obtained with the proposed approach is less than 2% compared to 84% when a correlation is not taken into account.