A generalization of the max-plus transformation, which is known as a methodto derive cellular automata from integrable equations, is proposed for complexnumbers. Operation rules for this transformation is also studied for generalnumber of complex variables. As an application, the max-plus transformation isapplied to the discrete Fourier transformation. Stretched coordinates areintroduced to obtain the max-plus transformation whose imaginary part coinsideswith a phase of the discrete Fourier transformation.
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