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This correspondence presents a novel approach for translational motion estimation based on the phase of the Fourier transform. It exploits the equality between the averaging of a group of successive frames and the convolution of the reference one with an impulse train function. The use of suitable space filling curves allows to reduce the error in motion estimation making the proposed approach robust under noise. Experimental results show that the proposed approach outperforms available techniques in terms of objective (PSNR) and subjective quality with a lower computational effort.