I am new to signal processing, and I am a bit confused by the use of coherence in academic literature. In several articles in neuroscience, coherence between signals (eg. EEG signals) is determined at a very high temporal resolution. See for an example this figure, from Bosman et al, 2012:
That article refers to the 'Communcation through coherence' theory from Fries, who describes coherence as:
"the pattern of phase-locking among oscillations in the communicating neuronal groups."
Bosman further states, it its experimental procedures:
" Spectral power, coherence, and GC influences were estimated by applying a fast Fourier transform (FFT) after multitapering (Mitra and Pesaran, 1999) with seven tapers. Given epoch lengths of 0.5 s, this resulted in a spectral smoothing of ±7 Hz. The resulting spectra are shown from 8 Hz to 140 Hz. We performed a separate analysis of the lower frequencies (4 Hz to 28 Hz), in which the same 0.5 s data epochs were Hanning tapered."
So if I understand it correctly, coherence is determined by looking at the stability of the phase difference between two signals over several tapers. But how can one then obtain values for the coherence at such high temporal resolutions? For each value, you would require several tapers; if I understand the description by Bosman correctly, this would result in a single value for coherence for each epoch of 0.5 seconds?
Bosman, C. A., Schoffelen, J. M., Brunet, N., Oostenveld, R., Bastos, A. M., Womelsdorf, T., ... & Fries, P. (2012). Attentional stimulus selection through selective synchronization between monkey visual areas. Neuron, 75(5), 875-888.
Fries, P. (2005). A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends in cognitive sciences, 9(10), 474-480.