The sunspot record for the time interval 1700-2001 can be considered as a sequence of independent, partly overlapping events, triggered quasi-periodically at intervals of the order of 11 years. The individual cycles are approximated by the step response of a band-pass dynamical system and the resulting model consists of the superposition of the response to a the independent pulses. The simulated sunspot data explain 98,4% of the cycle peak height variance and the residual standard deviation is 8,2 mean annual sunspots. A peak height of 117 for the solar cycle 23 occurring in 2000 is predicted, whereas the next cycle would start at about 2007 and will have a maximum around 111 in 2011. The model reproduces the high level of amplitude modulation in the interval 1950-2000 with a decrease afterwards. The model also recreates recurring sunspot minima and is linked to the phenomenon of the reversal of the solar magnetic field.