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A new approach to designing sets of ternary periodic signals with different periods for multi-input multi-output system identification is described. The signals are pseudo-random signals with uniform nonzero harmonics, generated from Galois field GF(q), where q is a prime or a power of a prime. The signals are designed to be uncorrelated, so that effects of different inputs can be easily decoupled. However, correlated harmonics can be included if necessary, for applications in the identification of ill-conditioned processes. A design table is given for q les 31. An example is presented for the design of five uncorrelated signals with a common period N = 168 . Three of these signals are applied to identify the transfer function matrix as well as the singular values of a simulated distillation column. Results obtained are compared with those achieved using two alternative methods.