📡 Signal Noise Simulation with Python

A Python project that demonstrates how Gaussian noise affects analog and digital signals using NumPy and Matplotlib.

This project was built as part of my learning journey to better understand the mathematics behind signal processing, including sine waves, Gaussian distributions, and data visualization.

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📖 Project Overview

Communication signals are often affected by noise during transmission. This simulation compares:

• Original Analog Signal
• Analog Signal with Gaussian Noise
• Original Digital Signal
• Digital Signal with Gaussian Noise

The goal is to visualize how noise impacts different types of signals and understand why digital communication is generally more resistant to interference.

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🚀 Technologies Used

• Python 3
• NumPy
• Matplotlib

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📚 Concepts Covered

• Analog Signals
• Digital Signals
• Sine Wave Generation
• Gaussian (Normal) Distribution
• Mean (μ)
• Standard Deviation (σ)
• Signal Noise Simulation
• Data Visualization

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🧮 Mathematical Model

Analog Signal

The analog signal is generated using the sine wave equation:

a(t)=sin(2πft)

where:

• f = Frequency (5 Hz)
• t = Time

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Gaussian Noise

Noise is generated using:

noise = np.random.normal(0, 0.3, len(t))

Where:

• Mean (μ) = 0

  • The average noise is centered around zero, so the signal is not shifted upward or downward.

• Standard Deviation (σ) = 0.3

  • Controls how much the signal is distorted.
  • Larger values produce stronger noise.

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📊 Simulation Output

The program generates four graphs:

1. Original Analog Signal
2. Analog Signal with Noise
3. Original Digital Signal
4. Digital Signal with Noise

(You can add a screenshot here after uploading it to the repository.)

Example:

![Signal Simulation](images/signal_noise.png)

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▶️ How to Run

Clone the repository:

git clone https://github.com/alexandrebayanza-maker/signal-noise-simulation.git

Move into the project folder:

cd signal-noise-simulation

Install the required libraries:

pip install numpy matplotlib

Run the program:

python analog_digital_simulation.py

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📂 Project Structure

signal-noise-simulation/
│
├── analog_digital_simulation.py
├── README.md
└── images/
    └── signal_noise.png

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What I Learned

Through this project, I learned:

• How analog and digital signals are represented mathematically.
• How Gaussian noise is generated using NumPy.
• The role of mean and standard deviation in probability distributions.
• Why digital signals are generally more resistant to noise.
• How data visualization makes complex concepts easier to understand.

This project reinforced an important lesson:

Programming becomes far more meaningful when you understand the mathematics behind the code.

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Future Improvements

Some enhancements I plan to add include:

• Adjustable signal frequency
• Interactive noise controls
• Signal filtering techniques
• Fast Fourier Transform (FFT) visualization
• Improved graphical interface

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👨‍💻 Author

Alexandre Bayanza

I'm passionate about software engineering, problem solving, and continuously learning through hands-on projects.

• LinkedIn: https://www.linkedin.com/in/alexandre-bayanza
• GitHub: https://github.com/alexandrebayanza-maker

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⭐ If you found this project interesting, feel free to star the repository or share your feedback!