Ramanujan's sum has been recently applied to detect different periodic components in 2D image. By filtering in frequency domain and obtaining the least common multiplier (lcm) of periodicity matrices, the basic 2D periodic pattern can be found. This paper introduces a multiplier-less structure to efficiently implement this process, based on the well-known number theoretic function called Möbius function. The relationship between impulse train and Ramanujan's sum is also clearly described, in both 1D and 2D cases.

中文翻译：

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拉马努金滤波器组莫比乌斯函数的二维有效无乘数结构

Ramanujan 的总和最近已应用于检测 2D 图像中的不同周期分量。通过在频域中进行滤波并获得周期矩阵的最小公倍数 (lcm)，可以找到基本的 2D 周期模式。本文基于称为 Möbius 函数的众所周知的数论函数，引入了一种无乘法器结构来有效地实现这一过程。在 1D 和 2D 情况下，也清楚地描述了脉冲串和拉马努金总和之间的关系。