A boundary value problem for a first-order hyperbolic equation with a nonlinear boundary condition is considered, which is used as a phenomenological model of a digital signal generator. The concept of a generalized periodic solution of a boundary value problem in the form of a piecewise-constant periodic wave is introduced and explicit formulas for such solutions are obtained. Using Sharkovsky's theorem, the question of the coexistence of generalized periodic solutions of different periods is investigated.

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