The mean annual sunspot record for the time interval 1700–2002 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 bandpass dynamical system and the resulting model consists of the superposition of the response to 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. An empirical linear relationship is found between the amplitude of the transfer function model for each cycle and the pulse interval of the preceding cycle that can be used as a tool of short-term forecasting of solar activity. A peak height of 112 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 110 in 2011. Cycle 24 is expected to have an annual mean peak value in the range 95 to 125. The model reproduces the high level of amplitude modulation in the interval 1950–2000 with a decrease afterwards, but the peak values for the cycles 18, 19, 21, and 22 are fairly underestimated. The semi-empirical model also recreates recurring sunspot minima and is linked to the phenomenon of the reversal of the solar magnetic field.