def _create_powerlaw(n_samples, fs, exponent):
"""Create a power law time series.
Parameters
----------
n_samples : int
The number of samples to simulate.
fs : float
Sampling rate of simulated signal, in Hz.
exponent : float
Desired power-law exponent, of the form P(f)=f^exponent.
Returns
-------
sig: 1d array
Time-series with the desired power law exponent.
Notes
-----
This function creates variable power law exponents by spectrally rotating white noise.
"""
# Start with white noise signal, that we will rotate, in frequency space
sig = np.random.randn(n_samples)
# Compute the FFT
fft_output = np.fft.fft(sig)
freqs = np.fft.fftfreq(len(sig), 1. / fs)
# Rotate spectrum and invert back to time series, with a z-score to normalize
# Delta exponent is divided by two, as the FFT output is in units of amplitude not power
fft_output_rot = rotate_powerlaw(freqs, fft_output, -exponent / 2)
sig = zscore(np.real(np.fft.ifft(fft_output_rot)))
return sig
def sim_powerlaw(n_seconds, fs, exponent=-2.0, f_range=None, **filter_kwargs):
"""Generate a power law time series with specified exponent by spectrally rotating white noise.
Parameters
----------
n_seconds : float
Simulation time, in seconds.
fs : float
Sampling rate of simulated signal, in Hz.
exponent : float
Desired power-law exponent, of the form P(f)=f^exponent.
f_range : list of [float, float] or None, optional
Frequency range to filter simulated data, as [f_lo, f_hi], in Hz.
**filter_kwargs : kwargs, optional
Keyword arguments to pass to `filter_signal`.
Returns
-------
sig: 1d array
Time-series with the desired power-law exponent.
"""
n_samples = int(n_seconds * fs)
sig = np.random.randn(n_samples)
# Compute the FFT
fft_output = np.fft.fft(sig)
freqs = np.fft.fftfreq(len(sig), 1. / fs)
# Rotate spectrum and invert, zscore to normalize.
# Note: the delta exponent to be applied is divided by two, as
# the FFT output is in units of amplitude not power
fft_output_rot = rotate_powerlaw(freqs, fft_output, -exponent/2)
sig = zscore(np.real(np.fft.ifft(fft_output_rot)))
if f_range is not None:
filter_signal(sig, fs, infer_passtype(f_range), f_range, **filter_kwargs)
return sig
###################################################################################################
# Spectral Rotation
# -----------------
#
# Another included utility function is spectral rotation, which rotates the power
# spectrum about a given axis frequency, by an amount indicated by the 'delta_exponent'
# argument (negative is clockwise, positive is counterclockwise).
#
# You can perform spectral rotation with
# :func:`~neurodsp.spectral.utils.rotate_powerlaw`.
#
#
# This function is mostly useful for investigating the effect of rotating the spectrum
# in frequency domain on the time domain signal. Effectively, this performs a very specific
# type of filtering with an ultra long filter kernel.
#
###################################################################################################
psd_rot = spectral.rotate_powerlaw(freq_med, psd_med, delta_exponent=-1, f_rotation=35)
plot_power_spectra([freq_med[:200], freq_med[:200]],
[psd_med[:200], psd_rot[:200]],
['Original', 'Rotated'])
###################################################################################################
#
# Sphinx settings:
# sphinx_gallery_thumbnail_number = 2
#
