A Fourier-Domain Framework for Generalized Signal Filtering and Denoising

Author: Daksh Saini

---

Project Overview

Noise contamination is a universal challenge in signal processing, affecting data integrity in fields ranging from biomedical engineering to astrophysics. Existing tools are often "domain-specific," relying on fixed noise models that fail when applied to novel datasets.

This project presents a General-Purpose Fourier-Domain Framework designed to democratize signal analysis. By leveraging the Fast Fourier Transform (FFT) and a modular filter design engine, this system provides a mathematically rigorous and computationally efficient tool for analyzing and denoising diverse one-dimensional datasets.

Key Capabilities

• Domain Agnostic: Proven effectiveness on ECG (Biomedical), P-waves (Seismic), and Audio signals.
• Spectral Precision: Manipulates signals in the frequency domain using $O(N \log N)$ FFT algorithms.
• Quantitative Validation: Built-in calculation of SNR (Signal-to-Noise Ratio), MSE (Mean Squared Error), and PSD (Power Spectral Density).

---

System Architecture

The framework is modularized into four distinct processing units:

1. Preprocessing Module: Handles normalization, detrending, and windowing (Hann/Hamming) to mitigate spectral leakage.
2. Spectral Transformation Core: Executes FFT/IFFT operations and computes magnitude/phase spectra.
3. Filter Design Unit: A configurable engine for creating digital filters:
   • Low-Pass / High-Pass (Butterworth & Ideal)
   • Band-Pass / Band-Stop
   • Notch Filters (Specific frequency rejection, e.g., 60Hz mains hum)
   • Adaptive Spectral Subtraction
4. Reconstruction & Evaluation: Rebuilds time-domain signals and computes error metrics.

---

Installation & Setup

Prerequisites

• OS: Windows, Linux, or macOS
• Python: Version 3.10 or higher
• RAM: Minimum 8 GB recommended

Quick Start

1. Clone the Repository:

   git clone [https://github.com/arachknight-daksh/Fourier_Tool.git](https://github.com/arachknight-daksh/Fourier_Tool.git)
   cd Fourier_Tool

2. Install Dependencies:

   pip install -r requirements.txt

3. Run Validation Script: Verify the core logic with the automated test suite:

   python run_validation.py

---

Usage Guide

Running the Jupyter Notebooks

The project includes a comprehensive 6-part notebook series demonstrating the theory and application:

jupyter notebook