Spectral properties of the x-ray pulses, generated by perfectly uniform cylindrical implosions of tungsten plasma with parameters typical of wire array z-pinches, are investigated under the simplifying assumption that the final stage of the kinetic-to-radiant energy conversion is not affected by the magnetic field. The x-ray emission is shown to be generated within a narrow (sub-micron) radiation-dominated stagnation shock front with a 'supercritical' amplitude. The structure of the stagnation shock is investigated using two independent radiation-hydrodynamics codes, and by constructing an approximate analytical model. The x-ray spectra are calculated for two values of the plasma column mass, 0.3 and 6 mg cm−1, with a newly developed two-dimensional radiation-hydrodynamics code RALEF-2D. The hard component of the spectrum (with a blackbody-fit temperature of 0.5–0.6 keV for the 6 mg cm−1 mass) originates from a narrow peak of the electron temperature inside the stagnation shock. The softer main component emerges from an extended halo, where the primary shock radiation is reemitted by colder layers of the imploding plasma. Our calculated x-ray spectrum for the 6 mg cm−1 tungsten column agrees well with the published Sandia experimental data (Foord et al 2004 Phys. Rev. Lett.93 055002).