File:Violet-noise-trace.svg

Summary

Description
English: Sampled trace of violet or purple noise, that is random noise with a power spectral density proportional to the frequency squared f². The plot was sampled from discrete Gaussian white noise, that was then spectrally filtered.
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(2)

"""
Note: Violet 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 *= frequencies # ~f amplitude spectrum
X = np.fft.irfft(fourier_amplitudes, n=nsamples, norm='ortho')
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(-3.2, 3.2)
plt.xlabel('t')
plt.ylabel('X')
plt.tight_layout()
plt.savefig('Violet-noise-trace.svg')

Licensing

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w:en:Creative Commons
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You are free:
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Under the following conditions:
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Category:CC-BY-SA-4.0#Violet-noise-trace.svg
Category:Self-published work Category:Violet noise
Category:CC-BY-SA-4.0 Category:Self-published work Category:Valid SVG created with Matplotlib code Category:Violet noise