Decomposing a signal into short-time narrow-banded modes

An algorithm for nonparametric decomposition of a signal into the sum of short-time narrow-banded modes (components) is introduced. Specifically, the signal data is augmented with its Hilbert transform to obtain the analytic signal. Then the set of constituent amplitude and frequency modulated (AM–FM) analytic sinusoids, each with slowly varying amplitude and frequency, is sought. The method for obtaining the short-time narrow-banded modes is derived by minimizing an objective function comprised of three criteria: smoothness of the instantaneous amplitude envelope, smoothness of the instantaneous frequency and complete reconstruction of the signal data. A minimum of the objective function is approached using a sequence of suboptimal updates of amplitude and phase. The updates are intuitive, efficient and simple to implement. For a given mode, the amplitude and phase are extracted from the band-pass filtered residual (signal after the other modes are removed), where the band-pass filter is applied about the previous modal instantaneous frequency estimate. The method is demonstrated by application to random output-only vibration data and order tracking data. It is demonstrated that vibration modal responses can be estimated from single channel data and order tracking can be performed without measured tachometer data.