Natural Frequency Identification of Rotating Blades From Single-Probe BTT Signals via a Periodically Extended Discrete Fourier Transform

A Periodically Extended Discrete Fourier Transform (PEDFT) is proposed to identify the natural frequencies of rotating blades from undersampled single-probe Blade Tip Timing (BTT) signals. Unlike conventional spectral analyses that suffer from aliasing due to low sampling rates and from sampling-rate variability across different rotational speeds, the PEDFT introduces a periodic extension strategy and a resolution alignment mechanism to reconstruct consistent vibration spectra. The periodic extension provides an intuitive framework for unfolding aliased components beyond the Nyquist limit, while the resolution alignment ensures uniform frequency grids under varying sampling conditions. This approach enables accurate cross-speed spectral comparison and natural-frequency identification using data from a single probe. Numerical simulations and experimental validation confirm that PEDFT achieves high accuracy and robust frequency estimation, offering enhanced practicality for single-probe BTT-based blade-vibration monitoring.