White Noise vs Colored Noise
1. What is White Noise?
White noise is a random signal that has equal power at all frequencies, meaning its power spectral density (PSD) is constant.
Snn(f) = Constant
Key Characteristics:
- Flat spectrum (all frequencies equally present)
- Ideal model (infinite bandwidth)
- Autocorrelation is an impulse
Rnn(Ï„) = σ² δ(Ï„)
Example: Thermal noise in electronic circuits is often approximated as white noise.
2. What is Colored Noise?
Colored noise is noise whose power is not uniformly distributed across frequencies. Its PSD varies with frequency.
General form:
Snn(f) ≠ Constant
Types of Colored Noise:
- Pink Noise: Power ∝ 1/f
- Brown Noise: Power ∝ 1/f²
- Blue Noise: Power ∝ f
These noises are called “colored” because their spectral shapes resemble different colors of light.
3. Differences
| Property | White Noise | Colored Noise |
|---|---|---|
| PSD | Constant | Frequency dependent |
| Frequency Content | All frequencies equally | Varies with frequency |
| Autocorrelation | Impulse (δ) | Spread over time |
| Example | Thermal noise | Pink noise, Brown noise |
4. Summary
In practice, perfectly white noise does not exist because infinite bandwidth is not physically possible. However, it is a very useful approximation in communication system analysis.