H ilbert Transform, Envelope, Instantaneous Phase, and Frequency

Abstract The application of the Hilbert transform to the signal analysis provides some additional information about amplitude, instantaneous phase, and frequency of vibrations. The Hilbert transform decomposition methods are intended for extracting simple components using the varying instantaneous frequency and amplitude from multicomponent nonstationary signals. The corresponding identification methods directly extract the backbone and damping curve of nonlinear vibration systems. This enables us to solve an inverse identification problem, namely, the problem of estimation of the initial nonlinear static elastic and damping force characteristics.