1. A method of monitoring vibration amplitude and frequency in a rotary machine, comprising the steps of:—receiving measurements of the vibration amplitude and the rotation speed of the machine; recording as a data point each amplitude measurement as a function of vibration frequency and rotational speed; storing a plurality of different amplitude thresholds each representing a noise floor for a respective one of a first set of sub-ranges of vibration frequency and rotational speed; comparing each amplitude measurement to the amplitude threshold for the sub-range of vibration frequency and rotational speed within which it falls; and determining the measurement as representing noise if it falls below the threshold and as significant spectral content if it is above the threshold.