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SPEC_PULS describes a suite of computer programs to simulate the emergent spectrum from a radially-pulsating star. It combines a Christy-type non-linear pulsation code with classical stellar atmosphere codes. The principal aim is to interpret the dynamical spectrum of the radially pulsating extreme helium star V652 Her, which shows a strong shock at minimum radius. The components are general enough to treat other classes of radial pulsation. The theoretical spectrum from a shocked pulsation model shows line doubling, with the blue component emerging at standstill velocity and accelerating blueward. The doubling phase depends on line depth and parent ion. The behaviour of line cores post-shock points to a drop in the ionization temperature, although the gas temperature in the model remains high. Shock compression leads to phase-dependent strengthening of Stark-broadened line wings, with the far wings responding first. With velocity, temperature and pressure-sensitive diagnostics, detailed tomography of the pulsation-driven shock in V652 Her seems possible. Even when no shock is present, the dynamical spectrum is significantly different from a model in hydrostatic equilibrium. Using the quasi-static approximation (e.g. at maximum radius) may lead to a considerable underestimate of the star's mean effective temperature and surface gravity.