A method of using a torsional vibration monitoring and diagnostics system coupled to a moving component, the method comprising: receiving from one or more sensors (110, 145), a time-variant signal representing a motion characteristic of the moving component; deriving from the time-variant signal, at various instants in time, a set of frequency-domain snapshots, each frequency-domain snapshot (221, 222, 223) of the set of frequency-domain snapshots representing an instantaneous frequency domain snapshot indicative of a spectral characteristic of the time-variant signal at a corresponding instant in time; processing the set of frequency-domain snapshots to derive information indicative of a torsional vibration characteristic of the moving component; providing a frequency-domain alarm threshold; comparing in real-time, each of the set of frequency-domain snapshots against the frequency-domain alarm threshold; generating one of a warning signal or an alarm signal when at least a portion of at least one of the set of frequency-domain snapshots exceeds the frequency-domain alarm threshold; wherein the frequency-domain alarm threshold is defined as a spectral envelope, characterized in that the frequency-domain alarm threshold is defined as a spectral envelope by using one or more averaged frequency domain snapshots, wherein each averaged frequency domain snapshot is an averaged version of multiple time-variant signal samples collected over a period of time; and in that the method further comprises: providing a timer; using the timer to determine a period of time during which at least a portion of the frequency-domain snapshots (221, 222, 223) in the set of frequency-domain snapshots exceeds the spectral envelope and transmitting the one of the warning signal or the alarm signal when the period of time exceeds a threshold time period set in the timer. receiving from one or more sensors (110, 145), a time-variant signal representing a motion characteristic of the moving component; deriving from the time-variant signal, at various instants in time, a set of frequency-domain snapshots, each frequency-domain snapshot (221, 222, 223) of the set of frequency-domain snapshots representing an instantaneous frequency domain snapshot indicative of a spectral characteristic of the time-variant signal at a corresponding instant in time; processing the set of frequency-domain snapshots to derive information indicative of a torsional vibration characteristic of the moving component; providing a frequency-domain alarm threshold; comparing in real-time, each of the set of frequency-domain snapshots against the frequency-domain alarm threshold; generating one of a warning signal or an alarm signal when at least a portion of at least one of the set of frequency-domain snapshots exceeds the frequency-domain alarm threshold; wherein the frequency-domain alarm threshold is defined as a spectral envelope, characterized in that the frequency-domain alarm threshold is defined as a spectral envelope by using one or more averaged frequency domain snapshots, wherein each averaged frequency domain snapshot is an averaged version of multiple time-variant signal samples collected over a period of time; and in that the method further comprises: providing a timer; using the timer to determine a period of time during which at least a portion of the frequency-domain snapshots (221, 222, 223) in the set of frequency-domain snapshots exceeds the spectral envelope and transmitting the one of the warning signal or the alarm signal when the period of time exceeds a threshold time period set in the timer. providing a timer; using the timer to determine a period of time during which at least a portion of the frequency-domain snapshots (221, 222, 223) in the set of frequency-domain snapshots exceeds the spectral envelope and transmitting the one of the warning signal or the alarm signal when the period of time exceeds a threshold time period set in the timer.