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This study presents a new glottal inverse filtering (GIF) technique based on the closed phase analysis over multiple fundamental periods. The proposed Quasi Closed Phase Analysis (QCP) method utilizes Weighted Linear Prediction (WLP) with a specific Attenuated Main Excitation (AME) weighting function that attenuates the contribution of the glottal source in the linear prediction model optimization. This enables the use of the autocorrelation criterion in linear prediction in comparison to the conventional covariance criterion used in the closed phase analysis. The proposed method was compared to previously developed methods by using a synthetic vowel database created with a physical modeling approach. The obtained objective measures show that the proposed method improves the GIF performance for both low- and high-pitched vowels.