This research presents the theory and implementation detail for the extraction of angular speed variations. In particular, bandpass filtering, frequency shifting and analytic representation are addressed with simple mathematical equations. Finally, some case studies on a 3kW induction motor are investigated for healthy and faulty conditions. Some vital key features and characteristics can be extracted from the angular speed variations. Pole pass speed side bands around the rotor speed can be used as a feature for broken rotor bar faults. The number of poles multiplied by the synchronous running speed cycles and the rise of 100 Hz components are key characteristics for voltage imbalance faults.