What Is (Colored) Noise in Signals? Types and Simple Examples : MALMIJAL-M Blog

Signal Processing Concepts and Engineering Insights.

Explore signal processing concepts, algorithm comparisons, and practical engineering insights.
Topics include FFT vs STFT, FRF analysis, filtering techniques, and other signal processing methods used in real engineering workflows.

Blog

What Is (Colored) Noise in Signals? Types and Simple Examples

In signal processing, noise refers to any unwanted disturbance that affects a signal.

It makes signals harder to analyze, interpret, or use.

What Is Noise in Signals

What Is Noise?

Noise is any undesired component added to a signal.

Example

Desired signal → clean sine wave
Noise → random background noise / environmental noise

Result: distorted signal

Intuition

“Noise = anything that hides the true signal”

Comparison of original waveform and noisy waveform

Why Noise Matters

Noise affects

Measurement accuracy
Signal interpretation
System performance

Real-world sources

Sensors
Environment
Electrical interference

Types of Noise

1. White Noise

Description

Random signal
Equal energy at all frequencies
Used for frequency excitation

Example

Background hiss in audio

2. Gaussian Noise

Description

Amplitude follows normal distribution
Often overlaps with white noise
Used for statistical modeling

Example

Sensor measurement noise
AGWN (Additive Gaussian White Noise)

3. Impulse Noise

Description

Sudden spikes
Short duration

Example

Electrical spikes
Data transmission errors

4. Periodic Noise

Description

Repeating pattern
Specific frequency components

Example

Power line interference (50/60 Hz)

Colored Noise (Frequency-Based Classification)

Colored noise is classified based on how its PSD(Power Spectral Density) varies with frequency

Colored noise

α = 0 → White noise
α = 1 → Pink noise
α = 2 → Brown (red) noise

Type	PSD Characteristic	Slope (dB/dec)	Behavior	Typical Use
White noise	α = 0, 1/f⁰	0	Equally energy at all frequencies	System identification, FRF measurement
Pink noise	α = 1, 1/f	-10	More energy at low frequencies, natural balance	Audio testing, acoustics
Brown noise	α = 2, 1/f²	-20	Dominated by very low frequencies	Random walk, environment modeling
Blue noise	α = -1, f	+10	High-frequency emphasized	Image processing (dithering)
Violet noise	α = -2, f²	+20	Strong high-frequency dominance	Specialized signal processing

Pink noise Brown noise

Identify Pink noise (Slope: -9.9) and Brown noise (Slope: -20) by slope

Identify Pink noise (Slope: -9.9) and Brown noise (Slope: -20) by slope

Ctrl+Shift+Mouse Click+Drag and Drop to analyze for selected region on the graph

How to Handle Noise

Noise handling is not only about removing unwanted components, but also about modeling and generating noise for analysis, testing, and system design.

1. Noise Reduction (Denoising)

Filtering Methods: reduce unwanted components while preserving the signal

MA(Moving Average) / EMA(Exponential Moving Average) → smoothing in time domain
FIR(Finite Impulse Response) / IIR(Infinite Impulse Response) filters → frequency-based noise removal
Band-pass / band-stop filters → isolate or suppress specific ranges

Detection Methods: identify and selectively remove abnormal noise

Z-score, IQR (Inter-Quartile Range) → outlier detection
Peak detection → remove impulse noise
Thresholding → eliminate extreme values

2. Noise Generation (Noise Injection / Modeling)

System Testing: add AWGN to test filter performance

Evaluate robustness
Validate algorithms under realistic conditions

Simulation & Modeling: Gaussian noise for measurement systems, brown noise for environment modeling

Reproduce real-world environments
Model sensor imperfections

Signal Processing Development: controlled SNR experiments

Benchmark denoising algorithms
Compare methods objectively

Excitation Signals: FRF measurement, system identification

White noise / pink noise used as input signals

Dithering

Add small noise intentionally
Reduce quantization error

3. Signal-to-Noise Ratio (SNR)

Noise handling is often evaluated using

SNR (Signal-to-Noise Ratio)

For example, if SNR = -6dB, noise power = 4*signal power or noise amplitude = 2*signal amplitude

Purpose

Measure signal quality
Compare processing methods

Key Takeaways

Noise = unwanted signal component
Different noise types require different methods
Noise can be reduced, detected, or generated
Understanding noise behavior is essential for both analysis and system design

Conclusions

Noise is an unavoidable part of real-world signals and represents any unwanted disturbance that obscures the true signal.

It directly impacts accuracy, interpretation, and system performance, making signal analysis more difficult
Different types of noise (white, Gaussian, impulse, periodic) have distinct characteristics, so no single solution works for all cases
Effective signal processing requires both removing unwanted noise and intelligently using noise when needed

In summary,
understanding the type and behavior of noise is essential for choosing the right processing approach and achieving reliable signal analysis.

Signal Processing Concepts and Engineering Insights.

Category

Digital Sampling & ConversionWhat Is (Colored) Noise in Signals? Types and Simple Examples

What Is (Colored) Noise in Signals? Types and Simple Examples

What Is Noise?

Why Noise Matters

Types of Noise

1. White Noise

2. Gaussian Noise

3. Impulse Noise

4. Periodic Noise

Colored Noise (Frequency-Based Classification)

How to Handle Noise

1. Noise Reduction (Denoising)

2. Noise Generation (Noise Injection / Modeling)

3. Signal-to-Noise Ratio (SNR)

Key Takeaways

Conclusions

Suggested Further Reading