File:Pink-noise-trace.svg

Summary

Description
English: Plot of sampled pink noise with a power spectral density of 1/f. The noise was created by random sampling of white noise and subsequent filtering in frequency space.
Date
Source Own work
Author Geek3
SVG development
InfoField
Source code
InfoField

Matplotlib source code

The plot was generated with Matplotlib
#! /usr/bin/env python3
# -*- coding:utf8 -*-

import matplotlib.pyplot as plt
import numpy as np
from math import *

plt.rcParams['font.sans-serif'] = 'DejaVu Sans'
np.random.seed(6)

"""
Note: pink noise is actually not so well depictable. As more higher frequency
componentes are added, the amplitude goes to infinity and will be dominated
by high-frequency noise. Thus, the image changes a lot with the cutoff sampling
density. We choose roughtly half a linewidth for sampling for a decent
appearance.
"""

nsamples = 501
t0 = 1.
t = np.linspace(0, t0, nsamples)

dt = t[1:] - t[:-1]
white_noise = np.random.normal(0, 1, nsamples)
fourier_amplitudes = np.fft.rfft(white_noise)
frequencies = np.fft.rfftfreq(nsamples, d=t[1] - t[0])

fourier_amplitudes[1:] /= np.sqrt(frequencies)[1:] # 1/sqrt(f) amplitude spectrum
X = np.fft.irfft(fourier_amplitudes, n=nsamples, norm='ortho')
X -= np.mean(X)
X /= np.std(X)

fig = plt.figure(figsize=(520 / 90.0, 340 / 90.0), dpi=72)
plt.plot(t, X)
plt.grid(True)
plt.xlim(t[0], t[-1])
plt.ylim(-3.5, 3.5)
plt.xlabel('t')
plt.ylabel('X')
plt.tight_layout()
plt.savefig('Pink-noise-trace.svg')

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Category:CC-BY-SA-4.0#Pink-noise-trace.svg
Category:Self-published work Category:Pink noise
Category:CC-BY-SA-4.0 Category:Pink noise Category:Self-published work Category:Valid SVG created with Matplotlib code