Method for analyzing the condition of a machine having a slowly rotating part, includes: rotating a rotatable part at a rotational speed of less than 50 rpm; generating an analogue electric measurement signal dependent on mechanical vibrations emanating from rotation of a shaft using a sensor having mechanical characteristics causing it to resonate at a certain resonance frequency; sampling the analogue measurement signal at a sampling frequency to generate a digital measurement data sequence in response to the received analogue measurement data; digitally filtering the digital measurement data sequence to obtain a filtered measurement signal and achieve a signal having a bandwidth between an upper and a lower frequency which is lower than the certain resonance frequency and the upper frequency being higher than the certain resonance frequency; generating a digitally enveloped signal in response to the filtered measurement signal by digitally rectifying the filtered measurement signal, and by digital low pass filtering of the rectified filtered measurement signal to generate the digitally enveloped signal; performing a condition analysis function for analyzing the condition of the machine dependent on the digitally enveloped signal.