This study proposes novel signal analysis methods for replay speech detection in automatic speaker verification (ASV) systems. The proposed methods -- arbitrary analysis (AA), mel scale analysis (MA), and constant Q analysis (CQA) -- are inspired by the calculation of the Fourier inversion formula. These methods introduce new perspectives in signal analysis for replay speech detection by employing alternative sinusoidal sequence groups. The efficacy of the proposed methods is examined on the ASVspoof 2019 \& 2021 PA databases with experiments, and confirmed by the performance of systems that incorporated the proposed methods; the successful integration of the proposed methods and a speech feature that calculates temporal autocorrelation of speech (TAC) from complex spectra strongly confirms it. Moreover, the proposed CQA and MA methods show their superiority to the conventional methods on efficiency (approximately 2.36 times as fast compared to the conventional constant Q transform (CQT) method) and efficacy, respectively, in analyzing speech signals, making them promising to utilize in music and speech processing works.