qnoise 1.0.1

Non-Gaussian colored noise generator

qNoise - Python Package

Non-Gaussian colored noise generator for Python.

Installation

pip install qnoise

Requirements

• Python ≥ 3.8
• NumPy ≥ 1.20
• C++11 compatible compiler

Platform-specific compiler setup:

• macOS: xcode-select --install
• Linux: sudo apt-get install build-essential (Debian/Ubuntu)
• Windows: Visual Studio Build Tools

Quick Start

import qnoise
import numpy as np
import matplotlib.pyplot as plt

# Seed for reproducibility
qnoise.seed_manual(42)

# Generate non-Gaussian colored noise
noise = qnoise.generate(tau=1.0, q=1.5, N=10000)

# Generate Gaussian colored noise (Ornstein-Uhlenbeck)
gauss_noise = qnoise.ornstein_uhlenbeck(tau=1.0, N=10000)

# Plot
plt.plot(noise[:1000])
plt.title('Non-Gaussian Colored Noise (q=1.5)')
plt.show()

Parameters

tau (autocorrelation time)

Controls temporal correlation:

• tau = 0: White noise (uncorrelated)
• tau > 0: Colored noise with correlation time tau

q (statistics parameter)

Controls distribution shape:

• q = 1: Gaussian (Ornstein-Uhlenbeck)
• q < 1: Sub-Gaussian (bounded support)
• q > 1: Supra-Gaussian (heavy tails)

Other parameters

• N: Number of samples to generate
• H: Integration time step (default: 0.01)
• temp_N: Transient samples to discard (default: auto-computed)

Functions

High-Level Interface

# Generate qNoise array
qnoise.generate(tau, q, N=1000, H=0.01, temp_N=-1, norm=False)

# Generate Ornstein-Uhlenbeck (Gaussian colored) noise
qnoise.ornstein_uhlenbeck(tau, N=1000, H=0.01, temp_N=-1, 
                          white_noise=False, ini_cond=0.0)

Low-Level Interface (Advanced)

For custom integration loops:

# Single integration steps
qnoise.qnoise_step(x, tau, q, H, sqrt_H)
qnoise.qnoise_norm_step(x, tau, q, H, sqrt_H)
qnoise.ornstein_uhlenbeck_step(x, tau, H)

# White noise
qnoise.gauss_white_noise()

# Random seed control
qnoise.seed_manual(seed)
qnoise.seed_timer()

Applications

• Algorithm robustness testing: Test ML models against realistic non-Gaussian noise
• Monte Carlo simulations: Financial risk models, reliability analysis
• Rare event simulation: Heavy-tailed noise for stress-testing
• Signal processing: Benchmark denoising algorithms
• Stochastic modeling: Complex systems with non-Gaussian dynamics

Examples

Compare Different Statistics

import qnoise
import matplotlib.pyplot as plt

qnoise.seed_manual(42)

fig, axes = plt.subplots(3, 2, figsize=(12, 10))

for i, q in enumerate([0.5, 1.0, 1.5]):
    # Time series
    noise = qnoise.generate(tau=1.0, q=q, N=10000)
    axes[i, 0].plot(noise[:1000])
    axes[i, 0].set_title(f'q={q} Time Series')
    
    # Distribution
    axes[i, 1].hist(noise, bins=50, density=True, alpha=0.7)
    axes[i, 1].set_title(f'q={q} Distribution')

plt.tight_layout()
plt.show()

Autocorrelation Analysis

import qnoise
import numpy as np
import matplotlib.pyplot as plt

qnoise.seed_manual(42)

# Generate noise with different correlation times
for tau in [0.1, 1.0, 10.0]:
    noise = qnoise.generate(tau=tau, q=1.0, N=50000)
    
    # Compute autocorrelation
    autocorr = np.correlate(noise - np.mean(noise), 
                           noise - np.mean(noise), 
                           mode='full')
    autocorr = autocorr[len(autocorr)//2:]
    autocorr /= autocorr[0]
    
    plt.plot(autocorr[:200], label=f'tau={tau}')

plt.xlabel('Lag')
plt.ylabel('Autocorrelation')
plt.legend()
plt.show()

Citation

If you use qNoise in your research, please cite:

@article{deza2022qnoise,
  title={qNoise: A generator of non-Gaussian colored noise},
  author={Deza, J. Ignacio and Ihshaish, Hisham},
  journal={SoftwareX},
  volume={18},
  pages={101034},
  year={2022},
  publisher={Elsevier},
  doi={10.1016/j.softx.2022.101034}
}

Links

• Paper: https://doi.org/10.1016/j.softx.2022.101034
• Demo: https://ignaciodeza.github.io/qNoise/
• GitHub: https://github.com/ignaciodeza/qNoise
• C++ Version: cpp/
• Go Version: go/

License

MIT License - see LICENSE file.

Author

J. Ignacio Deza
Senior Lecturer in Data Science
University of the West of England, Bristol
[e-mail]