🎵 Signal and Systems Project – Audio Denoising & Equalizer

📖 About

🎓Final Project of the Signal and Systems Course
👨‍🏫Under the supervision of Prof. Mohammad Rahmati
🍂Fall 2021 – Amirkabir University of Technology (Tehran Polytechnic)

This repository contains the implementation of a two-phase audio processing project focused on noise removal and frequency band equalization using Fourier analysis and digital filtering techniques.

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🎯 Phase 1: Audio Denoising

Objective

Remove noise from an audio signal (phaseIsample.wav) using Fourier Transform and frequency-domain filtering.

Steps Implemented

1. 🔊 Load and Visualize the audio signal (time domain)
2. 📈 Apply Fourier Transform to analyze frequency components
3. 🎚️ Identify Noise Frequencies – weaker amplitudes are considered noise
4. 🧹 Filter Out Noise by zeroing out non-dominant frequency components
5. 🔄 Apply Inverse Fourier Transform to reconstruct the denoised signal
6. 📊 Compare and Visualize original vs. denoised signals

Key Techniques

• Fast Fourier Transform (FFT)
• Frequency-domain filtering
• Inverse FFT for reconstruction

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🎛️ Phase 2: Simple Equalizer

Objective

Build a 10-band equalizer that amplifies or attenuates specific frequency bands based on user input.

Frequency Bands Used

• Band 1: 20–50 Hz
• Band 2: 50–100 Hz
• Band 3: 100–200 Hz
• Band 4: 200–500 Hz
• Band 5: 500–1000 Hz
• Band 6: 1000–2000 Hz
• Band 7: 2000–4000 Hz
• Band 8: 4000–8000 Hz
• Band 9: 8000–12000 Hz
• Band 10: 12000–20000 Hz

Steps Implemented

1. 🎚️ Define Gain Array – e.g., [2, 3, 1, 1, 0.2, 0.2, 0.1, 0.1, 0.1, 0.1]
2. 🔧 Apply Gains to corresponding frequency bands
3. 🔄 Reconstruct Signal using Inverse FFT
4. 💾 Export the modified audio file
5. 🎧 Compare original and equalized audio

Test Cases

• Case 1: Boost frequencies below 1200 Hz, attenuate others
• Case 2: Boost frequencies above 2000 Hz, attenuate others

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📦 Repository Structure

📂 Signal-And-Systems-Project/
├── 📄 p1.py # Phase 1: Denoising
├── 📄 p2.py # Phase 2: Equalizer
├── 📄 phaseIsample.wav # Sample audio for Phase 1
├── 📄 phase2sample.wav # Sample audio for Phase 2
├── 📄 Final_Project.pdf # Project description (Persian)
├── 📄 README.md # This file

🛠️ Technologies Used

• Python 🐍
• NumPy
• SciPy
• Matplotlib
• Wave module

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📊 Sample Results

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🧪 How to Run

1. Clone the repository:

   git clone https://github.com/Amirbehnam1009/Signal-And-Systems-Project.git

2. Install dependencies:

   pip install numpy scipy matplotlib

3. Run each phase:

   python p1.py
   python p2.py

📌 Notes

• This project was completed individually as part of the Signal and Systems course

• The report includes detailed explanations, visualizations, and analysis of each step

• The equalizer allows customizable gain control across 10 frequency bands

📬 Contact

For questions or collaborations, feel free to reach out: https://img.shields.io/badge/GitHub-Amirbehnam1009-blue

📜 License

This project is for educational purposes and is part of the academic curriculum at Amirkabir University of Technology.