Although Fourier-based methods have been standard methods for frequency analysis, they are not well suited for the analysis of nonlinear or non-stationary systems due to their time-varying natures. Thus, in this paper, a wavelet packet-based technique, which calculates time-varying coherence functions for input/output relationships, is developed. The developed method uses the Coiflet wavelet that has been widely used in signal processing. It is applied to obtain the time-varying coherence function, and to detect the impulse signal from the impulse-embedded signal such as an automobile sound/vibration signal with an external impact caused by a collision or passing over rough terrain. Some characteristics of non-stationary behavior such as the wavelet packet coefficients, maximum phase plane (MPP) analysis and fault detection are also demonstrated. The method gives promising results of non-stationary input-output systems, and so may be used as an effective tool for condition monitoring or fault detection area.