Phase slope index#

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_psi(data_1, data_2, nperseg_outer, fs, nperseg_inner, nfft, window, pad_type, f_min, f_max, f_step_sz=1, normalize=True)#

Calculates the phase slope index 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.
nperseg_outer – Outer window size. If normalize = False, this parameter is not used
fs – Sampling frequency.
nperseg_inner – Inner window size.
nfft – fft window size.
window – FFT window type. Supported window types are listed at https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html.
pad_type – Padding type, currently only “zero” padding is supported.
f_min – Minimum frequence for the evaluated interval.
f_max – Maximum frequence for the evaluated interval.
f_step_sz – Frequency step size in the evaluated interval.
normalize – Determines whether to normalize by dividing through the variance

Returns:

Connectivity between data1 and data 2 measured using the phase slope index.

Note

Use the following function for frequency domain data.

sfc.fd.run_psi(data_1, data_2, bins, f_min, f_max, f_step_sz=1)#

Calculates the phase slope index between two signals. Assumes data_1 and data_2 to be from time domain.

Parameters:

data1 – First dataset from the frequency domain domain; vector of frequency domain samples.
data2 – Second dataset from the frequency domain; vector of frequency domain samples.
bins – Frequency bins of the sample data.
f_min – Minimum frequence for the evaluated interval.
f_max – Maximum frequence for the evaluated interval.
f_step_sz – Frequency step size in the evaluated interval.

Returns:

Connectivity between data_1 and data_2 measured using the phase slope index.

Note

Use the following function for complex coherency domain data.

sfc.cd.run_psi(data, bins, f_min, f_max, f_step_sz=1)#

This function calculates the phase slope index between two signals.

Parameters:

data – List of outer window complex coherency estimates calculated from two signals.
bins – Frequency bins of the sample data.
f_min – Minimum frequence for the evaluated interval.
f_max – Maximum frequence for the evaluated interval.
f_step_sz – Frequency step size in the evaluated interval.

Returns:

Connectivity estimated based on the provided complex coherency measured using the phase slope index.

The following code example shows how to apply the phase slope index 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

    fmin = 28
    fmax = 33

    #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, fmin, fmax)
        conn_value_fd = calc_from_frequency_domain(signal_1, signal_2, frequency_sampling, fmin, fmax)
        conn_value_coh = calc_from_coherency_domain(signal_1, signal_2, frequency_sampling, fmin, fmax)

        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, f_min, f_max):
    nperseg_outer = int(frequency_sampling * 3)
    nperseg_inner = frequency_sampling
    nfft = frequency_sampling

    return td.run_psi(signal_1, signal_2, nperseg_outer, frequency_sampling, nperseg_inner, nfft, "hanning", "zero", f_min, f_max, f_step_sz = 1)

def calc_from_frequency_domain(signal_1, signal_2, frequency_sampling, f_min, f_max):
    nperseg_outer = int(frequency_sampling * 3)
    nperseg_inner = frequency_sampling
    nfft = frequency_sampling

    fd_signals_1 = list()
    fd_signals_2 = list()

    for idx_start in np.arange(0, len(signal_1), nperseg_outer):

        seg_data_X = misc._segment_data(signal_1[idx_start:int(idx_start + nperseg_outer)], nperseg_inner, pad_type = "zero")
        seg_data_Y = misc._segment_data(signal_2[idx_start:int(idx_start + nperseg_outer)], nperseg_inner, 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")

        fd_signals_1.append(fd_signal_1)
        fd_signals_2.append(fd_signal_2)

    return fd.run_psi(fd_signals_1, fd_signals_2, bins, f_min, f_max, 1)

def calc_from_coherency_domain(signal_1, signal_2, frequency_sampling, f_min, f_max):

    nperseg_outer = int(frequency_sampling * 3)
    nperseg_inner = frequency_sampling
    nfft = frequency_sampling

    data_coh = list()

    for idx_start in np.arange(0, len(signal_1), nperseg_outer):

        (bins, cc) = td.run_cc(signal_1[idx_start:(idx_start + nperseg_outer)], signal_2[idx_start:(idx_start + nperseg_outer)], nperseg_inner, pad_type = "zero",
                               fs = frequency_sampling, nfft = nfft, window = "hanning")
        data_coh.append(cc)

    return cohd.run_psi(data_coh, bins, f_min, f_max)

main()

The phase slope index is a reliable measure of connectivity which is commonly normalized via dividing a series of PSI estimates by their variance. Hence, the normalization increases the amount of data needed.

FiNNPY

Phase slope index#