Imaginary 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.

sfc.td.run_ic(data_1, data_2, fs, nperseg, nfft)#

Calculates the imaginary coherency between two signals. Assumes data_1 and data_2 to be from time domain.

Parameters:

data_1 – First dataset from time domain; vector of samples.
data_2 – Second dataset from time domain; vector of samples.
fs – Sampling frequency.
nperseg – Size of individual segments in fft.
nfft – fft window size.

Returns:

(bins, conn) - Frequency bins and corresponding imaginary coherency values.

Note

Use the following function for frequency domain data.

sfc.fd.run_ic(data_1, data_2)#

Calculates the imaginary coherency between two signals. Assumes data_1 and data_2 to be from the complex frequency domain.

Parameters:

data_1 – First dataset from the complex frequency domain; vector of samples.
data_2 – Second dataset from the complex frequency domain; vector of samples.

Returns:

Connectivity between data_1 and data_2 measured via imaginary coherence.

Note

Use the following function for complex coherency domain data.

sfc.cd.run_ic(data)#

Calculates the imaginary coherency between two signals. Assumes data_1 and data_2 to be from the complex frequency domain.

Parameters:: data – Complex coherency values; vector of samples.
Returns:: Connectivity estimated based on the provided complex coherency measured via the imaginary coherence.

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

import numpy as np

import matplotlib
matplotlib.use("Qt5agg")
import matplotlib.pyplot as plt

import finn.sfc.td as td
import finn.sfc.fd as fd
import finn.sfc.cd as cohd

import finn.sfc._misc as misc
import demo_data.demo_data_paths as paths

def main():
    data = np.load(paths.fct_sfc_data)
    frequency_sampling = 5500
    frequency_peak = 30

    noise_weight = 0.2

    phase_min = -90
    phase_max = 270
    phase_step = 4

    frequency_target = 30
    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_time_domain(signal_1, signal_2, frequency_sampling, nperseg, nfft, frequency_target)
        conn_value_coh = calc_from_time_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.show(block = True)


def calc_from_time_domain(signal_1, signal_2, frequency_sampling, nperseg, nfft, frequency_target):
    return td.run_ic(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 = misc._segment_data(signal_1, nperseg, pad_type = "zero")
    seg_data_Y = misc._segment_data(signal_2, nperseg, pad_type = "zero")

    (bins, fd_signal_1) = misc._calc_FFT(seg_data_X, frequency_sampling, nfft, window = "hanning")
    (_,    fd_signal_2) = misc._calc_FFT(seg_data_Y, frequency_sampling, nfft, window = "hanning")

    return fd.run_ic(fd_signal_1, fd_signal_2)[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) = td.run_cc(signal_1, signal_2, nperseg, "zero", frequency_sampling, nfft, "hanning")

    return cohd.run_ic(coh)[np.argmin(np.abs(bins - frequency_target))]


main()

The maximum score of imaginary coherence is dependent on the phase shift between two signals, hence it can only be interpreted relatively and never absolutely.

FiNNPY

Imaginary coherence#