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Retrieving object phase from the optical fringe pattern is a critical task in quantitative phase imaging and often requires appropriate image preprocessing (background and noise minimization), especially when retrieving phase from the single-shot fringe pattern image. In this article, for the first time, we propose to adapt the 2D Fast Iterative Filtering (FIF) method for fringe pattern decomposition and develop a novel version of FIF called the 2D fringe pattern Fast Iterative Filtering (fpFIF2), that is tailored for fringe pattern preprocessing. We show the positive influence of fpFIF2 onto fringe pattern filtering comparing to the previous 2D FIF implementation regarding processing speed, quality, and usage comfortability. We also compare the fpFIF2 with other state-of-the-art fringe pattern filtering methods in terms of aiding the Hilbert spiral transform method in phase retrieval. Employing numerical simulations and experimental fringe analysis, we prove that fpFIF2 outperforms reference methods, especially in terms of low-fringe-contrast phase reconstruction quality and decomposition time.