Time Series Simulations¶

This notebook introduces the time domain simulations used in this project.

Time series are simulated using neurodsp.

# Setup notebook state
from nbutils import setup_notebook; setup_notebook()

from neurodsp.sim import (sim_powerlaw, sim_synaptic_current, sim_knee,
                          sim_oscillation, sim_combined, sim_peak_oscillation)
from neurodsp.utils import set_random_seed
from neurodsp.plts import plot_time_series, plot_timeseries_and_spectra
from neurodsp.plts.utils import make_axes

# Import custom project code
from apm.io import APMDB
from apm.plts.utils import figsaver
from apm.sim.examples import get_times, get_examples

Settings¶

First, we will define some settings for the simulations.

# General simulation Settings
n_seconds = 10
fs = 500

# Component parameters
default_exp = -1.0
default_exp2 = -2.0
default_knee = 500
default_freq = 10
default_bw = 1.5
default_height = 1.5
f_range = (1, None)

# Collect together parameters for combined signals
comps_osc = {'sim_powerlaw' : {'exponent' : default_exp},
             'sim_oscillation' : {'freq' : default_freq}}
comps_burst = {'sim_powerlaw' : {'exponent' : default_exp},
               'sim_bursty_oscillation' : {'freq' : default_freq}}
peak_params = {'freq' : default_freq, 'bw' : default_bw, 'height' : default_height}

# Plot settings
plt_kwargs = {'xlabel' : '', 'ylabel' : ''}

# Settings for saving figures
SAVE_FIG = True
FIGPATH = APMDB().figs_path / '11_ts_sims'

# Create helper function to manage figsaver settings
fsaver = figsaver(SAVE_FIG, FIGPATH)

# Set random seed
set_random_seed(111)

Powerlaw Signal¶

First, we can simulate a ‘powerlaw’ signal, a 1/f signal that follow a powerlaw in the frequency domain.

# Simulate a powerlaw signal
sig_pow = sim_powerlaw(n_seconds, fs, default_exp, f_range=f_range)

# Plot simulated powerlaw signal and associated power spectrum
plot_timeseries_and_spectra(sig_pow, fs, **fsaver('powerlaw'))

../_images/11-TimeDomainSimulations_12_0.png

Continuous Oscillation¶

Next, we can simulate an oscillation, in this case, a continuous sinusoid.

# Simulate an oscillation
sig_osc = sim_oscillation(n_seconds, fs, freq=default_freq)

# Plot simulated oscillatory signal and associated power spectrum
plot_timeseries_and_spectra(sig_osc, fs, **fsaver('oscillation'))

../_images/11-TimeDomainSimulations_15_0.png

Combined Signal¶

Now we can can combine the aperiodic and periodic components from above, and create a combined signal.

# Simulate a combined signal, with an aperiodic and a periodic component
sig_comb = sim_combined(n_seconds, fs, comps_osc)

# Plot simulated combined and associated power spectrum
plot_timeseries_and_spectra(sig_comb, fs,  **fsaver('combined'))

../_images/11-TimeDomainSimulations_18_0.png

Synpatic Signal: Aperiodic Activity with a Knee¶

There are different possible ways to simulate aperiodic activity.

In this next simulation, we will simulate a ‘synpatic current’ model, which creates aperiodic activity with a knee.

# Simulate aperiodic activity from a synaptic current model
sig_syn = sim_synaptic_current(n_seconds, fs)

# Plot simulated synaptic signal and associated power spectrum
plot_timeseries_and_spectra(sig_syn, fs,  **fsaver('syn_current'))

../_images/11-TimeDomainSimulations_21_0.png

Aperiodic Signal with a Knee¶

We can also simulate signals with a knee without using ane explicit synaptic model.

# Simulate aperiodic activity from a synaptic current model
sig_knee = sim_knee(n_seconds, fs, 0, default_exp2, default_knee)

# Plot simulated knee signal and associated power spectrum
plot_timeseries_and_spectra(sig_knee, fs,  **fsaver('knee'))

../_images/11-TimeDomainSimulations_24_0.png

Bursty Oscillation¶

Oscillations are also not necessarily continuous. We we will simulate a combined signal with a bursty oscillation.

# Simulate a combined signal with a bursty oscillation
sig_burst = sim_combined(n_seconds, fs, comps_burst)

# Plot simulated bursty oscillatory signal and associated power spectrum
plot_timeseries_and_spectra(sig_burst, fs,  **fsaver('burst_osc'))

../_images/11-TimeDomainSimulations_27_0.png

Peak Signal¶

Another dimension that signals can vary in is the bandwidth of a peak. Here, we will create a simulation in which we can specify the bandwidth of an oscillatory peak, that is simulated on top of an aperiodic component.

# Simulate a signal with a peak of a defined bandwidth
sig_peak = sim_peak_oscillation(sig_pow, fs, **peak_params)

# Plot simulated peak signal and associated power spectrum
plot_timeseries_and_spectra(sig_peak, fs,  **fsaver('peak'))

../_images/11-TimeDomainSimulations_30_0.png

Example Time Series¶

In the notebooks that follow, you will see that measures are applied to a set of ‘example’ time series.

These examples are time series that have been pre-computed, using the functions above.

This set of example signals is shown here.

# Get example signals
times = get_times()
examples = get_examples()

# Plot example signals across different kinds of simulations
axes = make_axes(len(examples), 1, figsize=(10, 2 * len(examples)))
for ind, (label, sig) in enumerate(examples.items()):
    plot_time_series(times, examples[label], title=label, xlim=[5, 10], **plt_kwargs, ax=axes[ind])

../_images/11-TimeDomainSimulations_33_0.png

Aperiodic Methods

Time Series Simulations

Contents