A hand-held data collection and analyzing unit for collecting and analyzing vibration data induced by a rotating shaft including a processor that first converts the analog vibration signal into corresponding digital vibration samples. Thereafter, the processor provides in response to the digital vibration samples, corresponding output vibration samples in which samples within each set of output vibration samples are provided at a rate that varies as a function of variations in the speed of the rotating shaft. A digital processor then collects a time waveform record in response to a plurality of the output vibration samples, wherein the sample rate for the output vibration samples collected in the time waveform record varies as a function of variations in the speed of the rotating shaft.