  A generalization of the max-plus transformation, which is known as a method
to derive cellular automata from integrable equations, is proposed for complex
numbers. Operation rules for this transformation is also studied for general
number of complex variables. As an application, the max-plus transformation is
applied to the discrete Fourier transformation. Stretched coordinates are
introduced to obtain the max-plus transformation whose imaginary part coinsides
with a phase of the discrete Fourier transformation.
