Information transfer, measured by transfer entropy, is a key component of distributed computation. It is therefore important to understand the pattern of information transfer in order to unravel the distributed computational algorithms of a system. Since in many natural systems distributed computation is thought to rely on rhythmic processes a frequency resolved measure of information transfer is highly desirable. Here, we present a novel algorithm, and its efficient implementation, to identify separately frequencies sending and receiving information in a network. Our approach relies on the invertible maximum overlap discrete wavelet transform (MODWT) for the creation of surrogate data in the computation of transfer entropy and entirely avoids filtering of the original signals. The approach thereby avoids well-known problems due to phase shifts or the ineffectiveness of filtering in the information theoretic setting. We also show that measuring frequency-resolved information transfer is a partial information decomposition problem that cannot be fully resolved to date and discuss the implications of this issue. Last, we evaluate the performance of our algorithm on simulated data and apply it to human magnetoencephalography (MEG) recordings and to local field potential recordings in the ferret. In human MEG we demonstrate top-down information flow in temporal cortex from very high frequencies (above 100Hz) to both similarly high frequencies and to frequencies around 20Hz, i.e. a complex spectral configuration of cortical information transmission that has not been described before. In the ferret we show that the prefrontal cortex sends information at low frequencies (4-8 Hz) to early visual cortex (V1), while V1 receives the information at high frequencies (> 125 Hz).

通过传递熵衡量的信息传递是分布式计算的关键组成部分。因此，重要的是要了解信息传输的模式，以阐明系统的分布式计算算法。由于在许多自然系统中，分布式计算被认为依赖于节奏过程，因此非常需要信息传递的频率分辨量度。在这里，我们提出了一种新颖的算法及其有效的实现，以分别识别网络中发送和接收信息的频率。我们的方法依赖于可逆最大重叠离散小波变换（MODWT）在传递熵的计算中创建替代数据，并且完全避免了对原始信号的滤波。因此，该方法避免了由于相移或信息理论设置中的滤波无效而引起的众所周知的问题。我们还表明，测量频率分辨的信息传递是部分信息分解问题，迄今为止尚不能完全解决，并讨论了此问题的含义。最后，我们评估算法在模拟数据上的性能，并将其应用于人类脑磁图（MEG）记录以及雪貂中的局部磁场电势记录。在人类MEG中，我们演示了颞叶皮质中自顶向下的信息流，从非常高的频率（高于100Hz）到相似的高频以及大约20Hz左右的频率，即皮质信息传输的复杂频谱配置，之前没有进行过描述。