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Cartesian product files have been shown to exhibit attractive properties for partial match queries. The Disk Modulo (DM) allocation method is shown to have good performance on the distribution of Cartesian product files into an m-disk system. However, there was no explicit expression made before to represent the DM method's response time to a given partial match query. In this paper, based upon discrete Fourier transform, we derive one formula for such a computation. After obtaining this representation, the performance characteristics of the DM method can now be given an analytic interpretation. Some theoretical results are derived from this formula. We also use our formula to analyze the performance of several popular Disk Modulo algorithms.