Magnitude squared coherence

This function may be called for data in the time domain, the frequency domain, or (if correctly aligned) in the complex coherency domain.

Note

Use the following function for time domain data.

Note

Use the following function for frequency domain data.

Note

Use the following function for complex coherency domain data.

The following code example shows how to apply magnitude squared coherence to measure sfc.

import numpy as np

import matplotlib.pyplot as plt

import finnpy.feat.sfc as sfc  # @UnresolvedImport
import finnpy.demo.functionality.sfc.gen_demo_data as gen_demo_data  # @UnresolvedImport

def main():
   minimum_frequency = 13
   maximum_frequency = 27

   frequency_sampling = 2000
   time_s = 120
   offset_s = 1
   signal_length_samples = int(frequency_sampling * (time_s + offset_s * 2))
   data = gen_demo_data.gen_wn_signal(minimum_frequency, maximum_frequency, frequency_sampling, signal_length_samples)
   frequency_peak = (maximum_frequency + minimum_frequency)/2

   noise_weight = 0.2

   phase_min = -90
   phase_max = 270
   phase_step = 4

   frequency_target = 20
   nperseg = frequency_sampling
   nfft = frequency_sampling

   #Generate data
   offset = int(np.ceil(frequency_sampling/frequency_peak))
   loc_data = data[offset:]
   signal_1 = np.zeros((loc_data).shape)
   signal_1 += loc_data
   signal_1 += np.random.random(len(loc_data)) * noise_weight

   conn_vals = list()
   fig = plt.figure()
   for phase_shift in np.arange(phase_min, phase_max, phase_step):
      loc_offset = offset - int(np.ceil(frequency_sampling/frequency_peak * phase_shift/360))
      loc_data = data[(loc_offset):]
      signal_2 = np.zeros(loc_data.shape)
      signal_2 += loc_data
      signal_2 += np.random.random(len(loc_data)) * noise_weight

      plt.cla()
      plt.plot(signal_1[:500], color = "blue")
      plt.plot(signal_2[:500], color = "red")
      plt.title("Signal shifted by %2.f degree around %2.2fHz" % (float(phase_shift), float(frequency_peak)))
      plt.show(block = False)
      plt.pause(0.001)

      conn_value_td = calc_from_time_domain(signal_1, signal_2, frequency_sampling, nperseg, nfft, frequency_target)
      conn_value_fd = calc_from_frequency_domain(signal_1, signal_2, frequency_sampling, nperseg, nfft, frequency_target)
      conn_value_coh = calc_from_coherency_domain(signal_1, signal_2, frequency_sampling, nperseg, nfft, frequency_target)

      if (np.isnan(conn_value_td) == False and np.isnan(conn_value_fd) == False and np.isnan(conn_value_coh) == False):
         if (conn_value_td != conn_value_fd or conn_value_td != conn_value_coh):
            print("Error")

      conn_vals.append(conn_value_td if (np.isnan(conn_value_td) == False) else 0)

   plt.close(fig)

   plt.figure()
   plt.scatter(np.arange(phase_min, phase_max, phase_step), conn_vals)
   plt.ylim((0, 1.1))
   plt.show(block = True)


def calc_from_time_domain(signal_1, signal_2, frequency_sampling, nperseg, nfft, frequency_target):
   return sfc.msc_td(signal_1, signal_2, frequency_sampling, nperseg, nfft)[1][frequency_target]

def calc_from_frequency_domain(signal_1, signal_2, frequency_sampling, nperseg, nfft, frequency_target):
   seg_data_X = sfc._segment_data(signal_1, nperseg, pad_type = "zero")  # pylint: disable=protected-access
   seg_data_Y = sfc._segment_data(signal_2, nperseg, pad_type = "zero")  # pylint: disable=protected-access

   (bins, fd_signal_1) = sfc._calc_FFT(seg_data_X, frequency_sampling, nfft, window = "hanning")  # pylint: disable=protected-access
   (_,    fd_signal_2) = sfc._calc_FFT(seg_data_Y, frequency_sampling, nfft, window = "hanning")  # pylint: disable=protected-access

   return sfc.msc_fd(fd_signal_1, fd_signal_2, bins)[1][[np.argmin(np.abs(bins - frequency_target))]]

def calc_from_coherency_domain(signal_1, signal_2, frequency_sampling, nperseg, nfft, frequency_target):
   (bins, coh) = sfc.cc_td(signal_1, signal_2, nperseg, "zero", frequency_sampling, nfft, "hanning")

   return sfc.msc_cc(coh)[np.argmin(np.abs(bins - frequency_target))]


main()

Magnitude squared coherence is a very robust, but directionless, metric of coherence which is does not distinguish between real connectivity and volume conduction.