Generate Gaussian distributed noise with a power law spectrum with arbitrary exponents.
An exponent of two corresponds to brownian noise. Smaller exponents yield long-range correlations, i.e. pink noise for an exponent of 1 (also called 1/f noise or flicker noise).
Based on the algorithm in:
Timmer, J. and Koenig, M.: On generating power law noise. Astron. Astrophys. 300, 707-710 (1995)
Further reading: Colors of noise on Wikipedia
pip install colorednoise
- Python >= 3.6.15
- NumPy >= 1.17.0
Older Python 3 versions were not tested, but are likely to work. For Python 2 please use colorednoise version 1.x.
import colorednoise as cn
beta = 1 # the exponent
samples = 2**18 # number of samples to generate
y = cn.powerlaw_psd_gaussian(beta, samples)
# optionally plot the Power Spectral Density with Matplotlib
#from matplotlib import mlab
#from matplotlib import pylab as plt
#s, f = mlab.psd(y, NFFT=2**13)
#plt.loglog(f,s)
#plt.grid(True)
#plt.show()# generate several time series of independent indentically distributed variables
# repeat the simulation of each variable multiple times
import colorednoise as cn
n_repeats = 10 # repeat simulatons
n_variables = 5 # independent variables in each simulation
timesteps = 1000 # number of timesteps for each variable
y = cn.powerlaw_psd_gaussian(1, (n_repeats, n_variables, timesteps))
# the expected variance of for each variable is 1, but each realisation is different
print(y.std(axis=-1))# generate a broken power law spectrum: white below a frequency of
import colorednoise as cn
y = cn.powerlaw_psd_gaussian(1, 10**5, fmin=.05)
s, f = mlab.psd(y, NFFT=2**9)
#plt.loglog(f,s)
#plt.grid(True)
#plt.show()