def compute_cyclepoints(sig, fs, f_range, **find_extrema_kwargs):
"""Compute sample indices of cyclepoints.
Parameters
----------
sig : 1d array
Time series.
fs : float
Sampling rate, in Hz.
f_range : tuple of (float, float)
Frequency range, in Hz, to narrowband filter the signal. Used to find zero-crossings.
find_extrema_kwargs : dict, optional, default: None
Keyword arguments for the function to find peaks and troughs (:func:`~.find_extrema`)
that change filter parameters or boundary. By default, the boundary is set to zero.
Returns
-------
df_samples : pandas.DataFrame
Dataframe containing sample indices of cyclepoints.
Columns (listed for peak-centered cycles):
- ``peaks`` : signal indices of oscillatory peaks
- ``troughs`` : signal indices of oscillatory troughs
- ``rises`` : signal indices of oscillatory rising zero-crossings
- ``decays`` : signal indices of oscillatory decaying zero-crossings
- ``sample_peak`` : sample at which the peak occurs
- ``sample_zerox_decay`` : sample of the decaying zero-crossing
- ``sample_zerox_rise`` : sample of the rising zero-crossing
- ``sample_last_trough`` : sample of the last trough
- ``sample_next_trough`` : sample of the next trough
Examples
--------
Compute the signal indices of cyclepoints:
>>> from neurodsp.sim import sim_bursty_oscillation
>>> fs = 500
>>> sig = sim_bursty_oscillation(10, fs, freq=10)
>>> df_samples = compute_cyclepoints(sig, fs, f_range=(8, 12))
"""
# Ensure arguments are within valid range
check_param(fs, 'fs', (0, np.inf))
# Find extrema and zero-crossings locations in the signal
peaks, troughs = find_extrema(sig, fs, f_range, **find_extrema_kwargs)
rises, decays = find_zerox(sig, peaks, troughs)
# For each cycle, identify the sample of each extrema and zero-crossing
samples = {}
samples['sample_peak'] = peaks[1:]
samples['sample_last_zerox_decay'] = decays[:-1]
samples['sample_zerox_decay'] = decays[1:]
samples['sample_zerox_rise'] = rises
samples['sample_last_trough'] = troughs[:-1]
samples['sample_next_trough'] = troughs[1:]
df_samples = pd.DataFrame.from_dict(samples)
return df_samples
def test_extrema_interpolated_phase():
"""Test waveform phase estimate."""
# Load signal
signal = np.load(DATA_PATH + 'sim_stationary.npy')
Fs = 1000
f_range = (6, 14)
# Find peaks and troughs
Ps, Ts = cyclepoints.find_extrema(signal,
Fs,
f_range,
boundary=1,
first_extrema='peak')
# Find zerocrossings
zeroxR, zeroxD = cyclepoints.find_zerox(signal, Ps, Ts)
# Compute phase
pha = cyclepoints.extrema_interpolated_phase(signal,
Ps,
Ts,
zeroxR=zeroxR,
zeroxD=zeroxD)
assert len(pha) == len(signal)
assert np.all(np.isclose(pha[Ps], 0))
assert np.all(np.isclose(pha[Ts], -np.pi))
assert np.all(np.isclose(pha[zeroxR], -np.pi / 2))
assert np.all(np.isclose(pha[zeroxD], np.pi / 2))
def test_extrema_interpolated_phase(sim_stationary):
"""Test waveform phase estimate."""
sig = sim_stationary
fs = 1000
f_range = (6, 14)
# Find peaks and troughs
peaks, troughs = find_extrema(sig,
fs,
f_range,
boundary=1,
first_extrema='peak')
# Find zerocrossings
rises, decays = find_zerox(sig, peaks, troughs)
# Compute phase
pha = extrema_interpolated_phase(sig,
peaks,
troughs,
rises=rises,
decays=decays)
assert len(pha) == len(sig)
assert np.all(np.isclose(pha[peaks], 0))
assert np.all(np.isclose(pha[troughs], -np.pi))
assert np.all(np.isclose(pha[rises], -np.pi / 2))
assert np.all(np.isclose(pha[decays], np.pi / 2))
def test_plot_cyclepoints_array(sim_args):
peaks, troughs = find_extrema(sim_args['sig'], sim_args['fs'], (6, 14))
rises, decays = find_zerox(sim_args['sig'], peaks, troughs)
plot_cyclepoints_array(sim_args['sig'], sim_args['fs'], peaks=peaks, troughs=troughs,
rises=rises, decays=decays, save_fig=True,
file_name='test_plot_cyclepoints_array', file_path=TEST_PLOTS_PATH)
def test_plot_cyclepoints_array(sim_args):
ps, ts = find_extrema(sim_args['sig'], sim_args['fs'], (6, 14))
zerox_rise, zerox_decay = find_zerox(sim_args['sig'], ps, ts)
plot_cyclepoints_array(sim_args['sig'],
sim_args['fs'],
ps=ps,
ts=ts,
zerox_rise=zerox_rise,
zerox_decay=zerox_decay,
save_fig=True,
file_name='test_plot_cyclepoints_array',
file_path=TEST_PLOTS_PATH)
def test_compute_cyclepoints(sim_args):
sig = sim_args['sig']
fs = sim_args['fs']
f_range = sim_args['f_range']
peaks, troughs = find_extrema(sig, fs, f_range)
rises, decays = find_zerox(sig, peaks, troughs)
df_samples = compute_cyclepoints(sig, fs, f_range)
assert (df_samples['sample_peak'] == peaks[1:]).all()
assert (df_samples['sample_zerox_decay'] == decays[1:]).all()
assert (df_samples['sample_zerox_rise'] == rises).all()
assert (df_samples['sample_last_trough'] == troughs[:-1]).all()
assert (df_samples['sample_next_trough'] == troughs[1:]).all()
def test_find_zerox():
"""Test ability to find peaks and troughs."""
# Load signal
signal = np.load(DATA_PATH + 'sim_stationary.npy')
Fs = 1000
f_range = (6, 14)
# Find peaks and troughs
Ps, Ts = cyclepoints.find_extrema(signal,
Fs,
f_range,
boundary=1,
first_extrema='peak')
# Find zerocrossings
zeroxR, zeroxD = cyclepoints.find_zerox(signal, Ps, Ts)
assert len(Ps) == (len(zeroxR) + 1)
assert len(Ts) == len(zeroxD)
assert Ps[0] < zeroxD[0]
assert zeroxD[0] < Ts[0]
assert Ts[0] < zeroxR[0]
assert zeroxR[0] < Ps[1]
def compute_features(sig,
fs,
f_range,
center_extrema='P',
burst_detection_method='cycles',
burst_detection_kwargs=None,
find_extrema_kwargs=None,
hilbert_increase_n=False):
"""Segment a recording into individual cycles and compute features for each cycle.
Parameters
----------
sig : 1d array
Voltage time series.
fs : float
Sampling rate, in Hz.
f_range : tuple of (float, float)
Frequency range for narrowband signal of interest (Hz).
center_extrema : {'P', 'T'}
The center extrema in the cycle.
- 'P' : cycles are defined trough-to-trough
- 'T' : cycles are defined peak-to-peak
burst_detection_method : {'cycles', 'amp'}
Method for detecting bursts.
- 'cycles': detect bursts based on the consistency of consecutive periods & amplitudes
- 'amp': detect bursts using an amplitude threshold
burst_detection_kwargs : dict, optional
Keyword arguments for function to find label cycles as in or not in an oscillation.
find_extrema_kwargs : dict, optional
Keyword arguments for function to find peaks an troughs (:func:`~.find_extrema`)
to change filter Parameters or boundary.By default, it sets the filter length to three
cycles of the low cutoff frequency (``f_range[0]``).
hilbert_increase_n : bool, optional, default: False
Corresponding kwarg for :func:`~neurodsp.timefrequency.hilbert.amp_by_time`.
If true, this zero-pads the signal when computing the Fourier transform, which can be
necessary for computing it in a reasonable amount of time.
Returns
-------
df : pandas.DataFrame
Dataframe containing features and identifiers for each cycle. Each row is one cycle.
Columns (listed for peak-centered cycles):
- ``sample_peak`` : sample of 'sig' at which the peak occurs
- ``sample_zerox_decay`` : sample of the decaying zero-crossing
- ``sample_zerox_rise`` : sample of the rising zero-crossing
- ``sample_last_trough`` : sample of the last trough
- ``sample_next_trough`` : sample of the next trough
- ``period`` : period of the cycle
- ``time_decay`` : time between peak and next trough
- ``time_rise`` : time between peak and previous trough
- ``time_peak`` : time between rise and decay zero-crosses
- ``time_trough`` : duration of previous trough estimated by zero-crossings
- ``volt_decay`` : voltage change between peak and next trough
- ``volt_rise`` : voltage change between peak and previous trough
- ``volt_amp`` : average of rise and decay voltage
- ``volt_peak`` : voltage at the peak
- ``volt_trough`` : voltage at the last trough
- ``time_rdsym`` : fraction of cycle in the rise period
- ``time_ptsym`` : fraction of cycle in the peak period
- ``band_amp`` : average analytic amplitude of the oscillation
computed using narrowband filtering and the Hilbert
transform. Filter length is 3 cycles of the low
cutoff frequency. Average taken across all time points
in the cycle.
- ``is_burst`` : True if the cycle is part of a detected oscillatory burst
- ``amp_fraction`` : normalized amplitude
- ``amp_consistency`` : difference in the rise and decay voltage within a cycle
- ``period_consistency`` : difference between a cycle’s period and the period of the
adjacent cycles
- ``monotonicity`` : fraction of instantaneous voltage changes between consecutive
samples that are positive during the rise phase and negative during the decay phase
Notes
-----
Peak vs trough centering
- By default, the first extrema analyzed will be a peak, and the final one a trough.
- In order to switch the preference, the signal is simply inverted and columns are renamed.
- Columns are slightly different depending on if ``center_extrema`` is set to 'P' or 'T'.
"""
# Set defaults if user input is None
if burst_detection_kwargs is None:
burst_detection_kwargs = {}
warnings.warn('''
No burst detection parameters are provided. This is not recommended.
Check your data and choose appropriate parameters for "burst_detection_kwargs".
Default burst detection parameters are likely not well suited for the data.
''')
if find_extrema_kwargs is None:
find_extrema_kwargs = {'filter_kwargs': {'n_cycles': 3}}
else:
# Raise warning if switch from peak start to trough start
if 'first_extrema' in find_extrema_kwargs.keys():
raise ValueError('''
This function assumes that the first extrema identified will be a peak.
This cannot be overwritten at this time.''')
# Negate signal if to analyze trough-centered cycles
if center_extrema == 'P':
pass
elif center_extrema == 'T':
sig = -sig
else:
raise ValueError(
'Parameter "center_extrema" must be either "P" or "T"')
# Find peak and trough locations in the signal
ps, ts = find_extrema(sig, fs, f_range, **find_extrema_kwargs)
# Find zero-crossings
zerox_rise, zerox_decay = find_zerox(sig, ps, ts)
# For each cycle, identify the sample of each extrema and zero-crossing
shape_features = {}
shape_features['sample_peak'] = ps[1:]
shape_features['sample_zerox_decay'] = zerox_decay[1:]
shape_features['sample_zerox_rise'] = zerox_rise
shape_features['sample_last_trough'] = ts[:-1]
shape_features['sample_next_trough'] = ts[1:]
# Compute duration of period
shape_features['period'] = shape_features['sample_next_trough'] - \
shape_features['sample_last_trough']
# Compute duration of peak
shape_features['time_peak'] = shape_features['sample_zerox_decay'] - \
shape_features['sample_zerox_rise']
# Compute duration of last trough
shape_features['time_trough'] = zerox_rise - zerox_decay[:-1]
# Determine extrema voltage
shape_features['volt_peak'] = sig[ps[1:]]
shape_features['volt_trough'] = sig[ts[:-1]]
# Determine rise and decay characteristics
shape_features['time_decay'] = (ts[1:] - ps[1:])
shape_features['time_rise'] = (ps[1:] - ts[:-1])
shape_features['volt_decay'] = sig[ps[1:]] - sig[ts[1:]]
shape_features['volt_rise'] = sig[ps[1:]] - sig[ts[:-1]]
shape_features['volt_amp'] = (shape_features['volt_decay'] +
shape_features['volt_rise']) / 2
# Compute rise-decay symmetry features
shape_features[
'time_rdsym'] = shape_features['time_rise'] / shape_features['period']
# Compute peak-trough symmetry features
shape_features['time_ptsym'] = shape_features['time_peak'] / \
(shape_features['time_peak'] + shape_features['time_trough'])
# Compute average oscillatory amplitude estimate during cycle
amp = amp_by_time(sig,
fs,
f_range,
hilbert_increase_n=hilbert_increase_n,
n_cycles=3)
shape_features['band_amp'] = [
np.mean(amp[ts[sig_idx]:ts[sig_idx + 1]])
for sig_idx in range(len(shape_features['sample_peak']))
]
# Convert feature dictionary into a DataFrame
df = pd.DataFrame.from_dict(shape_features)
# Define whether or not each cycle is part of a burst
if burst_detection_method == 'cycles':
df = detect_bursts_cycles(df, sig, **burst_detection_kwargs)
elif burst_detection_method == 'amp':
df = detect_bursts_df_amp(df, sig, fs, f_range,
**burst_detection_kwargs)
else:
raise ValueError('Invalid entry for "burst_detection_method"')
# Rename columns if they are actually trough-centered
if center_extrema == 'T':
rename_dict = {
'sample_peak': 'sample_trough',
'sample_zerox_decay': 'sample_zerox_rise',
'sample_zerox_rise': 'sample_zerox_decay',
'sample_last_trough': 'sample_last_peak',
'sample_next_trough': 'sample_next_peak',
'time_peak': 'time_trough',
'time_trough': 'time_peak',
'volt_peak': 'volt_trough',
'volt_trough': 'volt_peak',
'time_rise': 'time_decay',
'time_decay': 'time_rise',
'volt_rise': 'volt_decay',
'volt_decay': 'volt_rise'
}
df.rename(columns=rename_dict, inplace=True)
# Need to reverse symmetry measures
df['volt_peak'] = -df['volt_peak']
df['volt_trough'] = -df['volt_trough']
df['time_rdsym'] = 1 - df['time_rdsym']
df['time_ptsym'] = 1 - df['time_ptsym']
return df
#################################################################################################### # # 2. Localize rise and decay midpoints # ------------------------------------ # # In addition to localizing the peaks and troughs of a cycle, we also want to get more information # about the rise and decay periods. For instance, these flanks may have deflections if the peaks or # troughs are particularly sharp. In order to gauge a dimension of this, we localize midpoints for # each of the rise and decay segments. These midpoints are defined as the times at which the voltage # crosses halfway between the adjacent peak and trough voltages. If this threshold is crossed # multiple times, then the median time is chosen as the flank midpoint. This is not perfect; # however, this is rare, and most of these cycles should be removed by burst detection. from bycycle.cyclepoints import find_zerox zeroxR, zeroxD = find_zerox(signal_low, Ps, Ts) #################################################################################################### tlim = (13, 14) tidx = np.logical_and(t >= tlim[0], t < tlim[1]) tidxPs = Ps[np.logical_and(Ps > tlim[0] * Fs, Ps < tlim[1] * Fs)] tidxTs = Ts[np.logical_and(Ts > tlim[0] * Fs, Ts < tlim[1] * Fs)] tidxDs = zeroxD[np.logical_and(zeroxD > tlim[0] * Fs, zeroxD < tlim[1] * Fs)] tidxRs = zeroxR[np.logical_and(zeroxR > tlim[0] * Fs, zeroxR < tlim[1] * Fs)] plt.figure(figsize=(12, 2)) plt.plot(t[tidx], signal_low[tidx], 'k') plt.plot(t[tidxPs], signal_low[tidxPs], 'b.', ms=10) plt.plot(t[tidxTs], signal_low[tidxTs], 'r.', ms=10) plt.plot(t[tidxDs], signal_low[tidxDs], 'm.', ms=10)
def compute_features(x, Fs, f_range,
center_extrema='P',
burst_detection_method='cycles',
burst_detection_kwargs=None,
find_extrema_kwargs=None,
hilbert_increase_N=False):
"""
Segment a recording into individual cycles and compute
features for each cycle
Parameters
----------
x : 1d array
voltage time series
Fs : float
sampling rate (Hz)
f_range : tuple of (float, float)
frequency range for narrowband signal of interest (Hz)
center_extrema : {'P', 'T'}
The center extrema in the cycle
'P' : cycles are defined trough-to-trough
'T' : cycles are defined peak-to-peak
burst_detection_method: {'consistency', 'amp'}
Method for detecting bursts
'cycles': detect bursts based on the consistency of consecutive periods and amplitudes
'amp': detect bursts using an amplitude threshold
burst_detection_kwargs : dict | None
Keyword arguments for function to find label cycles
as in or not in an oscillation
find_extrema_kwargs : dict | None
Keyword arguments for function to find peaks and
troughs (cyclepoints.find_extrema) to change filter
parameters or boundary.
By default, it sets the filter length to three cycles
of the low cutoff frequency (`f_range[0]`)
hilbert_increase_N : bool
corresponding kwarg for filt.amp_by_time
If true, this zeropads the signal when computing the
Fourier transform, which can be necessary for
computing it in a reasonable amount of time.
Returns
-------
df : pandas.DataFrame
dataframe containing several features and identifiers
for each cycle. Each row is one cycle.
Columns (listed for peak-centered cycles):
- sample_peak : sample of 'x' at which the peak occurs
- sample_zerox_decay : sample of the decaying zerocrossing
- sample_zerox_rise : sample of the rising zerocrossing
- sample_last_trough : sample of the last trough
- sample_next_trough : sample of the next trough
- period : period of the cycle
- time_decay : time between peak and next trough
- time_rise : time between peak and previous trough
- time_peak : time between rise and decay zerocrosses
- time_trough : duration of previous trough estimated by zerocrossings
- volt_decay : voltage change between peak and next trough
- volt_rise : voltage change between peak and previous trough
- volt_amp : average of rise and decay voltage
- volt_peak : voltage at the peak
- volt_trough : voltage at the last trough
- time_rdsym : fraction of cycle in the rise period
- time_ptsym : fraction of cycle in the peak period
- band_amp : average analytic amplitude of the oscillation
computed using narrowband filtering and the Hilbert
transform. Filter length is 3 cycles of the low
cutoff frequency. Average taken across all time points
in the cycle.
- is_burst : True if the cycle is part of a detected oscillatory burst
Notes
-----
Peak vs trough centering
- By default, the first extrema analyzed will be a peak,
and the final one a trough. In order to switch the preference,
the signal is simply inverted and columns are renamed.
- Columns are slightly different depending on if 'center_extrema'
is set to 'P' or 'T'.
"""
# Set defaults if user input is None
if burst_detection_kwargs is None:
burst_detection_kwargs = {}
warnings.warn('''
No burst detection parameters are provided.
This is very much not recommended.
Please inspect your data and choose appropriate
parameters for "burst_detection_kwargs".
Default burst detection parameters are likely
not well suited for your desired application.
''')
if find_extrema_kwargs is None:
find_extrema_kwargs = {'filter_kwargs': {'N_cycles': 3}}
else:
# Raise warning if switch from peak start to trough start
if 'first_extrema' in find_extrema_kwargs.keys():
raise ValueError('''This function has been designed
to assume that the first extrema identified will be a peak.
This cannot be overwritten at this time.''')
# Negate signal if to analyze trough-centered cycles
if center_extrema == 'P':
pass
elif center_extrema == 'T':
x = -x
else:
raise ValueError('Parameter "center_extrema" must be either "P" or "T"')
# Find peak and trough locations in the signal
Ps, Ts = find_extrema(x, Fs, f_range, **find_extrema_kwargs)
# Find zero-crossings
zeroxR, zeroxD = find_zerox(x, Ps, Ts)
# For each cycle, identify the sample of each extrema and zerocrossing
shape_features = {}
shape_features['sample_peak'] = Ps[1:]
shape_features['sample_zerox_decay'] = zeroxD[1:]
shape_features['sample_zerox_rise'] = zeroxR
shape_features['sample_last_trough'] = Ts[:-1]
shape_features['sample_next_trough'] = Ts[1:]
# Compute duration of period
shape_features['period'] = shape_features['sample_next_trough'] - \
shape_features['sample_last_trough']
# Compute duration of peak
shape_features['time_peak'] = shape_features['sample_zerox_decay'] - \
shape_features['sample_zerox_rise']
# Compute duration of last trough
shape_features['time_trough'] = zeroxR - zeroxD[:-1]
# Determine extrema voltage
shape_features['volt_peak'] = x[Ps[1:]]
shape_features['volt_trough'] = x[Ts[:-1]]
# Determine rise and decay characteristics
shape_features['time_decay'] = (Ts[1:] - Ps[1:])
shape_features['time_rise'] = (Ps[1:] - Ts[:-1])
shape_features['volt_decay'] = x[Ps[1:]] - x[Ts[1:]]
shape_features['volt_rise'] = x[Ps[1:]] - x[Ts[:-1]]
shape_features['volt_amp'] = (shape_features['volt_decay'] + shape_features['volt_rise']) / 2
# Comptue rise-decay symmetry features
shape_features['time_rdsym'] = shape_features['time_rise'] / shape_features['period']
# Compute peak-trough symmetry features
shape_features['time_ptsym'] = shape_features['time_peak'] / (shape_features['time_peak'] + shape_features['time_trough'])
# Compute average oscillatory amplitude estimate during cycle
amp = amp_by_time(x, Fs, f_range, hilbert_increase_N=hilbert_increase_N, filter_kwargs={'N_cycles': 3})
shape_features['band_amp'] = [np.mean(amp[Ts[i]:Ts[i + 1]]) for i in range(len(shape_features['sample_peak']))]
# Convert feature dictionary into a DataFrame
df = pd.DataFrame.from_dict(shape_features)
# Define whether or not each cycle is part of a burst
if burst_detection_method == 'cycles':
df = detect_bursts_cycles(df, x, **burst_detection_kwargs)
elif burst_detection_method == 'amp':
df = detect_bursts_df_amp(df, x, Fs, f_range, **burst_detection_kwargs)
else:
raise ValueError('Invalid entry for "burst_detection_method"')
# Rename columns if they are actually trough-centered
if center_extrema == 'T':
rename_dict = {'sample_peak': 'sample_trough',
'sample_zerox_decay': 'sample_zerox_rise',
'sample_zerox_rise': 'sample_zerox_decay',
'sample_last_trough': 'sample_last_peak',
'sample_next_trough': 'sample_next_peak',
'time_peak': 'time_trough',
'time_trough': 'time_peak',
'volt_peak': 'volt_trough',
'volt_trough': 'volt_peak',
'time_rise': 'time_decay',
'time_decay': 'time_rise',
'volt_rise': 'volt_decay',
'volt_decay': 'volt_rise'}
df.rename(columns=rename_dict, inplace=True)
# Need to reverse symmetry measures
df['volt_peak'] = -df['volt_peak']
df['volt_trough'] = -df['volt_trough']
df['time_rdsym'] = 1 - df['time_rdsym']
df['time_ptsym'] = 1 - df['time_ptsym']
return df
#
# 2. Localize rise and decay midpoints
# ------------------------------------
#
# In addition to localizing the peaks and troughs of a cycle, we also want to get more information
# about the rise and decay periods. For instance, these flanks may have deflections if the peaks or
# troughs are particularly sharp. In order to gauge a dimension of this, we localize midpoints for
# each of the rise and decay segments. These midpoints are defined as the times at which the voltage
# crosses halfway between the adjacent peak and trough voltages. If this threshold is crossed
# multiple times, then the median time is chosen as the flank midpoint. This is not perfect;
# however, this is rare, and most of these cycles should be removed by burst detection.
#
# Note: Plotting midpoints and extrema may also be performed using the dataframe output from
# :func:`~.compute_features` with the :func:`~.plot_cyclepoints` function.
rises, decays = find_zerox(sig_low, peaks, troughs)
plot_cyclepoints_array(sig_low,
fs,
xlim=(13, 14),
peaks=peaks,
troughs=troughs,
rises=rises,
decays=decays)
####################################################################################################
#
# 3. Compute features of each cycle
# ---------------------------------
# After these 4 points of each cycle are localized, we compute some simple statistics for each
# cycle. The main cycle-by-cycle function, compute_features(), returns a table (pandas.DataFrame)
####################################################################################################
#
# 2. Localize rise and decay midpoints
# ------------------------------------
#
# In addition to localizing the peaks and troughs of a cycle, we also want to get more information
# about the rise and decay periods. For instance, these flanks may have deflections if the peaks or
# troughs are particularly sharp. In order to gauge a dimension of this, we localize midpoints for
# each of the rise and decay segments. These midpoints are defined as the times at which the voltage
# crosses halfway between the adjacent peak and trough voltages. If this threshold is crossed
# multiple times, then the median time is chosen as the flank midpoint. This is not perfect;
# however, this is rare, and most of these cycles should be removed by burst detection.
from bycycle.cyclepoints import find_zerox
zerox_rise, zerox_decay = find_zerox(sig_low, ps, ts)
####################################################################################################
tlim = (13, 14)
tidx = np.logical_and(times >= tlim[0], times < tlim[1])
tidx_ps = ps[np.logical_and(ps > tlim[0] * fs, ps < tlim[1] * fs)]
tidx_ts = ts[np.logical_and(ts > tlim[0] * fs, ts < tlim[1] * fs)]
tidx_ds = zerox_decay[np.logical_and(zerox_decay > tlim[0] * fs,
zerox_decay < tlim[1] * fs)]
tidx_rs = zerox_rise[np.logical_and(zerox_rise > tlim[0] * fs,
zerox_rise < tlim[1] * fs)]
plt.figure(figsize=(12, 2))
plt.plot(times[tidx], sig_low[tidx], 'k')
plt.plot(times[tidx_ps], sig_low[tidx_ps], 'b.', ms=10)