Envelope analysis is a widely used tool for fault detection in rotating machines. In envelope analysis, impulsive noise contaminates the measured signal, making it difficult to extract the features of defects. This paper proposes a time–frequency envelope analysis that overcomes the effects of impulsive noises. Envelope analysis is performed by dividing the signal into several sections through a time window. The effect of impulsive noises is eliminated by using the frequency characteristics of the short time rectangular wave. The proposed method was verified through simulation and experimental data. The simulation was conducted by mathematically modeling a cyclo-stationary process that characterizes rotating machinery signals. In addition, the effectiveness of the method was verified by the measured data of normal and defective air-conditioners produced on the actual assembly line. This simple proposed method is effective enough to detect the faults. In the future, the approaches of big data and deep learning will be required for the development of the prognostic health-management framework.