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This paper presents a fundamental spatial performance limitation analysis method for multiple array paper machine cross-directional (CD) processes based on a two-dimensional (temporal and spatial) frequency decomposition method. Paper machine CD processes are spatially-distributed dynamical systems. Due to their (almost) spatially invariant characteristic, the models of these systems are considered as transfer matrices with rectangular circulant matrix blocks, whose input and output singular vectors are the Fourier components of dimension equivalent to number of actuators and measurements respectively. Through this method, a fundamental spatial performance limitation of multiple array CD processes can be observed. A real industrial multiple array CD process is used for illustrating the effectiveness of this method.