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add_colored_noise

Absolutely! Here's the expanded and fully updated documentation for add_colored_noise, now including the new features like:

  • fs (sampling rate) for realistic frequency scaling
  • Support for additional noise colors (blue, violet)
  • Support for custom spectral filters (callables)
  • Return of isolated noise for analysis
  • Time-varying envelopes

add_colored_noise

Location: noise/noise_addition.py

Description

add_colored_noise introduces colored noise into a signal using frequency-domain filtering techniques. It simulates real-world interference by allowing users to define spectral characteristics, noise intensity, and modulation envelopes for non-stationary noise.

This function is especially useful for: - Creating realistic signal variations - Stress-testing algorithms under different noise conditions - Signal augmentation for machine learning and data-driven modeling

✨ New Features

  • fs (sampling rate) parameter ensures accurate spectral shaping
  • Supports blue and violet noise profiles
  • Accepts custom frequency-domain filters as callables
  • Returns isolated noise component for separate inspection
  • Applies modulation envelope to simulate time-varying noise

Notes

  • White noise → flat power across all frequencies
  • Pink noise → power ∝ 1/f (natural, biological systems)
  • Brown noise → power ∝ 1/f² (emphasizes low frequencies)
  • Blue noise → power ∝ f (emphasizes high frequencies)
  • Violet noise → power ∝ f² (extreme high-frequency boost)
  • Custom filters can target specific frequency patterns (e.g., harmonic peaks)

Parameters

  • wave (np.ndarray):
    The input signal to which noise will be added.

  • fs (float):
    Sampling rate in Hz. Used to compute correct frequency bins for spectral shaping.

  • noise_power (float):
    Base noise power (variance). Determines energy of the added noise.

  • npw (tuple(float, float)):
    Range multiplier for noise power. Adds variability in intensity.
    Example: (0.8, 1.2) allows ±20% fluctuation.

  • mf (tuple(float, float)):
    Range for amplitude modulation applied to the entire signal.
    Simulates slight scaling due to environmental or hardware changes.

  • color (str or callable, optional):
    Defines the spectral profile of the noise. Options:

  • 'white' → flat spectrum
  • 'pink' → 1/f
  • 'brown' → 1/f²
  • 'blue' → f
  • 'violet' → f²

  • Callable → custom function filter(freqs) that returns a frequency-domain mask
    (e.g., harmonic peaks or band-limited filters)

  • mod_envelope (dict, optional):
    Modulates the noise amplitude over time (non-stationary noise). Should include:

  • 'func': an envelope function like envelope_sine, envelope_random_walk, etc.
  • 'param': parameter(s) passed to the envelope function (usually a range)
    Example: {'func': envelope_sine, 'param': [0.01, 0.015]}. More parameter examples provided in config.py.
  • If None, noise remains stationary. Default: None.

Returns

  • res (np.ndarray):
    Final signal with colored, possibly modulated noise added.

  • noise (np.ndarray):
    The noise component alone (useful for plotting, denoising tests, etc.)

Example Usage

import numpy as np
import SigVarGen as svg

# Create a clean sine wave
fs = 1000  # Hz
t = np.linspace(0, 1, fs, endpoint=False)
clean_signal = np.sin(2 * np.pi * 5 * t)

# Define parameters
noise_power = 0.05
npw_range = (1.0, 1.2)
mf_range = (1.0, 1.0)

# Add blue noise with sine-modulated envelope
noisy_signal, noise = svg.add_colored_noise(
    wave=clean_signal,
    fs=fs,
    noise_power=noise_power,
    npw=npw_range,
    mf=mf_range,
    color='blue',
    mod_envelope={'func': svg.envelope_sine, 'param': [0.01, 0.02]}
)

# Optional: plot or analyze the noise separately
print("Noisy Signal:", noisy_signal[:10])
print("Isolated Noise:", noise[:10])