A procedure for analysis of radial artery pulse signal is described. The procedure is used to estimate the diagnostic significance of different signal parameters in analyses using increasingly complex algorithms. The procedure can be used to elucidate and employ typological features of the signal shape and the spectral functions for some signal parameters of time series. At every step of the procedure, a particular parameter set is chosen. It is the informative set at this step that is important for diagnostically significant decision rules construction for the disease under consideration. A multi-step pulse signal analysis procedure was implemented with respect to diagnostic problem of identification of early stage pediatric arterial hypertension. This identification was based on large-scale experimental material received during clinical survey. Three analysis stages are described: signal shape analysis, analysis of spectral density shape of quasi-periodic time series, and analysis of spectral density parameters of pulse signal dicrotic wave time series. The multi-step pulse signal analysis procedure allows the reliability of early stage pediatric arterial hypertension identification to be increased significantly.