"""
.. _sec-pw-wavy:
Shift in frequency (sine waves)
====================================================================================================
Description
----------------------------------------------------------------------------------------------------
This function simulates a sum-of-sine signal :math:`y_t=\sin(2\pi f_1 t)+\sin(2\pi f_2 t)` where :math:`t=0,\dots,T-1`.
The frequency vector :math:`[f_1, f_2]` alternates between :math:`[0.075, 0.1]` and :math:`[0.1, 0.125]` at each change point index.
Gaussian white noise can be added to the signal.
.. figure:: /images/sum_of_sines.png
:scale: 50 %
:alt: Signal example
Top: signal example. Bottom: associated spectrogram.
Usage
----------------------------------------------------------------------------------------------------
Start with the usual imports and create a signal.
.. code-block:: python
import numpy as np
import matplotlib.pylab as plt
import ruptures as rpt
# creation of data
n, dim = 500, 3 # number of samples, dimension
n_bkps, sigma = 3, 5 # number of change points, noise standart deviation
signal, bkps = rpt.pw_wavy(n, n_bkps, noise_std=sigma)
rpt.display(signal, bkps)
Code explanation
----------------------------------------------------------------------------------------------------
.. autofunction:: ruptures.datasets.pw_wavy.pw_wavy
"""
from itertools import cycle
import numpy as np
from numpy.random import normal
from ruptures.utils import draw_bkps
[docs]def pw_wavy(n_samples=200, n_bkps=3, noise_std=None):
"""Return a 1D piecewise wavy signal and the associated changepoints.
Args:
n_samples (int, optional): signal length
n_bkps (int, optional): number of changepoints
noise_std (float, optional): noise std. If None, no noise is added
Returns:
tuple: signal of shape (n_samples, 1), list of breakpoints
"""
# breakpoints
bkps = draw_bkps(n_samples, n_bkps)
# we create the signal
f1 = np.array([0.075, 0.1])
f2 = np.array([0.1, 0.125])
freqs = np.zeros((n_samples, 2))
for sub, val in zip(np.split(freqs, bkps[:-1]), cycle([f1, f2])):
sub += val
tt = np.arange(n_samples)
# DeprecationWarning: Calling np.sum(generator) is deprecated
# Use np.sum(np.from_iter(generator)) or the python sum builtin instead.
signal = np.sum([np.sin(2 * np.pi * tt * f) for f in freqs.T], axis=0)
if noise_std is not None:
noise = normal(scale=noise_std, size=signal.shape)
signal += noise
return signal, bkps