Wavelet transform is a powerful technique well suited to non-stationary signal processing. The properties of wavelet are determined by its basis function. In the fields of modal analysis, mechanical condition monitoring and fault diagnosis, impulse responses or transient responses are very common signals to be analyzed. The Laplace wavelet is a single-sided damped exponential wavelet and is a desirable wavelet basis to analyze signals of impulse response. A correlation filtering approach is introduced using the Laplace wavelet to identify the impulse response from vibration signals. Successful results are obtained in identifying the natural frequency of a hydro-generator shaft, and diagnosing the wear fault of intake valve of an internal combustion engine.