In order to discriminate small changes for early fault diagnosis of rotating machines, condition monitoring demands that the measurement of instantaneous angular speed (IAS) of the machines be as accurate as possible. This paper develops the theoretical basis and practical implementation of IAS data acquisition and IAS estimation when noise influence is included. IAS data is modelled as a frequency modulated signal of which the signal-to-noise ratio can be improved by using a high-resolution encoder. From this signal model and analysis, optimal configurations for IAS data collection are addressed for high accuracy IAS measurement. Simultaneously, a method based on analytic signal concept and fast Fourier transform is also developed for efficient and accurate estimation of IAS. Finally, a fault diagnosis is carried out on an electric induction motor driving system using IAS measurement. The diagnosis results show that using a high-resolution encoder and a long data stream can achieve noise reduction by more than 10 dB in the frequency range of interest, validating the model and algorithm developed. Moreover, the results demonstrate that IAS measurement outperforms conventional vibration in diagnosis of incipient faults of motor rotor bar defects and shaft misalignment.