In the domain of frequency sweeping interferometry, the accurate extraction of distance information from nonlinear frequency scanning signals holds paramount significance in ensuring meticulous measurements of high precision. This paper presents a novel, to the best of our knowledge, high-speed distance extraction algorithm based on the table lookup method and validates its feasibility through theoretical models, simulations, and practical experiments. The proposed algorithm achieves comparable accuracy to traditional methods involving resampling and Hilbert transform. However, it outperforms them in robustness against noise and variations in sampling points. This method can accurately process signals sampled even below the Nyquist sampling rate. The simplicity and computational efficiency of the proposed approach make it suitable for various nonlinear sampling applications, promising broad applicability in scientific and engineering contexts.