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This paper considers the problem of fusing two low-rate sensors (e.g., microphones) for reconstructing one high-resolution signal when time delay of arrival (TDOA) is present as well. We show that under certain conditions the phase of the cross-spectrum-density of low-rate measurements becomes independent of the signal in the high-rate front end of the system. We then utilize this fact to demonstrate that it is possible to extend a class of TDOA estimation techniques known as the generalized cross correlation technique to linear-phase multi-rate sensor systems. Finally, we illustrate how the combination of the theory of linear-phase multi-rate filter banks and TDOA estimation can result in a practical, multi-sensor signal reconstruction system.