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As real-time signal analysis is required for fast processing, several recursive algorithms were proposed to perform the calculation with overlapping sequences in a sliding manner. One Sliding DFT (SDFT) method is the Hopping DFT (HDFT), where the DFT calculations are not evaluated sample-by-sample but with longer steps, thus further reducing the computational complexity compared to the other SDFT algorithms. This letter analyses the effect of fixed-point roundoff error in the HDFT algorithm, including the Updating Vector Transform (UVT) block. A closed-form expression for the resulting quantization noise power at the output of the HDFT algorithm is provided, which is validated through simulations. 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