Colored noise

A noise signal is produced by a stochastic process. The color of noise, also called the noise spectrum, refers to the power spectrum of a noise signal.

The practice of naming kinds of noise after colors started with white noise, a signal whose spectrum has equal power within any equal interval of frequencies. That name was given by analogy with white light, which was (incorrectly) assumed to have such a flat power spectrum over the visible range. Other color names, such as pink, red, and blue were then given to noise with other spectral profiles, often (but not always) in reference to the color of light with similar spectra. Some of those names have standard definitions in certain disciplines, while others are very informal and poorly defined.

Source: Wikipedia

import numpy as np
from matplotlib import pyplot as plt

from stimuli.audio import Noise

In this tutorial, we will create and plot the power spectrum of different noise colors. simple-stimuli implements several noise color in Noise. Refer to the documentation of the color argument for available colors.

colors = ("white", "pink", "blue", "violet", "brown")
sounds = dict()
for color in colors:
    # identical volume on all audio channels
    sounds[color] = Noise(volume=10, color=color)

We can listen to each individual noise by playing each sound with play().

for sound in sounds.values():
    sound.play(blocking=True)

The underlying signal is stored in the signal attribute. The returned numpy array has 2 dimensions: (n_samples, n_channels). As the volume has been set identicaly on all audio channels, we can disregard the second dimension and select only the first channel.

plt.figure()
for color in colors:
    signal = sounds[color].signal[:, 0]  # retrieve the signal
    # compute the one-dimensional discrete fourier transform
    frequencies = np.fft.rfftfreq(signal.size)
    dft = np.abs(np.fft.rfft(signal))
    # plot with log scaling on both X and Y axis
    plt.loglog(frequencies, dft)
plt.legend(colors)
plt.ylim([1e-3, None])
plt.show()

Estimated memory usage: 17 MB