Algorithm for Determination of Thresholds of Significant Coherence in Time-Frequency Analysis.

A quantitative assessment of the level of coherence between two signals is important in many applications. Two biomedically relevant cases are Transfer Function Analysis (TFA) of Cerebral Autoregulation (CA) and Coherent Hemodynamics Spectroscopy (CHS), where the first signal is Arterial Blood Pressure (ABP) and the second signal is either cerebral Blood Flow Velocity (BFV) or cerebral hemoglobin concentration. To determine the time intervals and frequency bands in which the signals are significantly coherent, a coherence threshold is required. This threshold of significant coherence can be found using multiple samples of surrogate data to generate a distribution of coherence. Then the 95 percentile of the distribution can be used as the threshold corresponding to a significance level α = 0.05. However, storing the entire coherence distribution uses a large amount of computer memory. To address this problem, we have developed an algorithm to determine the coherence threshold with little memory usage. A subfield of data streaming algorithms is devoted to finding quantiles using little memory. This work does not aim to find a new streaming algorithm but rather to develop an algorithm that can be tailored to the needs of applications such as TFA and CHS. The algorithm presented here identifies the coherence thresholds for a wavelet scaleogram using much less memory then what would be required to store the entire coherence distribution.