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In this paper, the sampling theorem for bandlimited functions over    domains is generalized to one over ∏    domains. The generalized theorem is applicable to the experimental design model in which each factor has a different number of levels and enables us to estimate the parameters in the model by using Fourier transforms. Moreover, the relationship between the proposed sampling theorem and orthogonal arrays is also provided.

A Generalized Sampling Theorem Over Galois Field Domains for Experimental Design