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The theorems of identical relation for interpolation and decimation in the linear canonical transform (LCT) domain have been proposed in this paper. For improving the efficiency of sampling rate conversion and saving the memory in digital system, we propose two identical relations in sampling rate conversion, one in interpolation and the other one in decimation. The result shows that the two identical relations can properly secure the sampling rate conversion and reduce the operating works significantly. The simulation results are also presented to show the correctness of the proposed theorems. These two identical relations can be widely used in sampling rate conversion in the LCT domain.