The signals that can be obtained from rotating machines often convey the information of machine. For example, whether the machine under investigation has faults or not, these signals often can be well expressed by pulse signals. Therefore the ability to detect of the fault signal would be major concern of fault diagnosis of rotating machine. Conventional cepstrum has been widely used in echo and fault detection. But one of the problems of finding impulse signal using the conventional cepstrum is that it is normally very sensitive to signal to noise ratio (SNR). In this thesis, a signal processing method to detect impulse signal in noisy environment is proposed. Because the proposed method minimizes signal power at a cepstrum domain, we propose to call 'Minimum Variance (MV) cepstrum'. Computer simulations have been performed to understand the characteristics of the MV cepstrum. Fault detection of ball bearing systems has been based on the idea to detect periodicities of impulse trains due to faults. In this regard, we designed the experiment on the bearing system that has various types of faults. Both the simulation and experiment confirmed that the MV cepstrum is a useful technique to detect impulse in noisy environment.