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We propose a 2D representation in the frequency-decay factor plane of an arbitrary real-world vibration signal. The signal is expressed as the sum of a decayed-attenuation sine term modulated by an amplitude function and a noise residue. We extend the combined approach of Capon estimation and amplitude and phase estimation (CAPES) to damped real vibration signals (DR-CAPES). In the proposed DR-CAPES method, the high-resolution amplitude and phase are estimated simultaneously for both angular frequency and decay factor grids. The performance of the proposed approach is tested numerically with noisy vibration data. Results show that the DR-CAPES method has an excellent frequency resolution, which helps to overcome difficulties in spectrum estimation when vibration modes are very close, and a small bias, which makes it suitable for obtaining accurate amplitude spectrums. The results also indicate that the proposed method can accurately estimate the amplitude spectrum with the use of averaging and denoising processes.

Damped CAPES 2D Spectral Estimation for Real-Valued Vibration Signals