In this paper, we propose a new algorithm, the irrational-window-filter projection method (IWFPM), for solving arbitrary dimensional global quasiperiodic systems. Based on the projection method, IWFPM further utilizes the concentrated distribution of Fourier coefficients to filter out relevant spectral points using an irrational window. Moreover, a corresponding index-shift transform is designed to make the Fast Fourier Transform available. The corresponding error analysis on the function approximation level is also given. We apply IWFPM to 1D, 2D, and 3D quasiperiodic Schr\"odinger eigenproblems to demonstrate its accuracy and efficiency. For both extended and localized quantum states, IWFPM exhibits a significant computational advantage over PM. Furthermore, the widespread existence of such spectral point distribution feature can endow IWFPM with significant potential for broader applications in quasiperiodic systems.

翻译：本文提出一种新算法——无理窗滤波投影方法（IWFPM），用于求解任意维全局准周期系统。基于投影方法，IWFPM进一步利用傅里叶系数的集中分布特性，通过无理窗过滤相关谱点。同时，设计相应的索引平移变换以实现快速傅里叶变换的可用性。文中还给出了函数逼近层面的误差分析。我们将IWFPM应用于一维、二维和三维准周期薛定谔特征值问题，以验证其精度与效率。对于扩展态和局域态量子态，IWFPM相比PM均展现出显著的计算优势。此外，此类谱点分布特征的普遍存在性，使IWFPM在准周期系统中具有广泛应用的巨大潜力。