低频噪声信号处理中的Ramanujan和
Ramanujan sums for signal processing of low frequency noise
摘要：
非周期（低频）频谱可能源自算术函数（如莫比乌斯函数或曼戈尔特函数）的平均值中的误差项，这些函数是素数的编码序列。在离散傅里叶变换中，分析波是周期性的，不太适合表示低频区域。在这里，我们介绍了一个新的信号处理工具的基础上的Ramanujan和c_q（n），以及适用于分析的算术序列与许多共振p/q。的总和是准周期的谐振的时间n和非周期的谐振的顺序q。新的结果出现从使用这种拉马努金-傅里叶变换（RFT）的上下文中的算术和实验信号
英文摘要：
An aperiodic (low frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Möbius function or Mangoldt function, which are coding sequences for prime numbers. In the discrete Fourier transform the analyzing wave is periodic and not well suited to represent the low frequency regime. In place we introduce a new signal processing tool based on the Ramanujan sums c_q(n), well adapted to the analysis of arithmetical sequences with many resonances p/q. The sums are quasi-periodic versus the time n of the resonance and aperiodic versus the order q of the resonance. New results arise from the use of this Ramanujan-Fourier transform (RFT) in the context of arithmetical and experimental signals
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