  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 (PM), 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. IWFPM exhibits a
significant computational advantage over PM for both extended and localized
quantum states. Furthermore, the widespread existence of such spectral point
distribution feature can endow IWFPM with significant potential for broader
applications in quasiperiodic systems.
