Frequency-Independent Centroid Frequency Shift Method for Signal Attenuation Estimation

Signal attenuation estimation is a critical task in signal processing and is essential for analyzing media characteristics and compensating for energy loss. Current centroid frequency shift (CFS)-based methods for estimating attenuation are mostly based on the assumptions of full-band analysis and frequency-dependent or -independent quality factor (Q). In this article, we propose a novel frequency-independent CFS (FiCFS) method for signal attenuation estimation with higher adaptability. It is based on arbitrary frequency bands instead of the full-band spectrum defined by the conventional CFS method, and accordingly, the derivation is performed by incomplete gamma functions instead of ordinary gamma functions. Through rigorous mathematical derivations, the first moment (centroid frequency) and the second moment (variance) are proved to be frequency insensitive for arbitrary frequency bands, and then the arbitrary frequency band-based CFS method, i.e., the FiCFS method, is derived with the frequency-weighted exponential spectrum assumption. The matching ability of the frequency-weighted exponential spectrum to other signal spectra is verified, demonstrating the method's adaptability to most attenuated signals. Experimental results using synthetic and field datasets demonstrate that the proposed method is adaptive, noise-immune, and reliable.