Zero-Phase Digital Filter in Pure C

📌 Project Overview

This project implements a zero-phase digital IIR filter in pure C language, aiming to achieve the same numerical precision as:

• MATLAB filtfilt()
• Python scipy.signal.filtfilt()

Filter coefficients are designed using MATLAB/Python and exported to C for embedded-level execution.

The goal is to reproduce high-precision zero-phase filtering behavior in a lightweight, portable C implementation.

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🚀 Motivation

In many embedded and biomedical signal processing applications (e.g., EEG, ECG, PPG), phase distortion is unacceptable.

The standard solution in high-level environments is:

filtfilt() → forward-backward filtering

However, MATLAB and Python implementations cannot be directly deployed to embedded systems.

This project provides:

• A pure C zero-phase IIR filter
• Edge padding compensation
• Initial condition calculation
• Precision benchmarking against MATLAB and Python

If you need more technical details, please refer to my blog: C语言实现IIR型零相位带通滤波器

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🧠 Core Features

1️⃣ Zero-Phase Filtering

We implement forward-backward filtering:

1. Forward filtering
2. Reverse signal
3. Backward filtering

This eliminates phase distortion.

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2️⃣ Edge Compensation Strategy

To avoid edge distortion, we use:

• Symmetric edge padding
• Proper initial state computation

This ensures numerical stability and minimizes transient artifacts.

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3️⃣ Precision Benchmark

We compare outputs among:

• MATLAB filtfilt()
• Python scipy.signal.filtfilt()
• Pure C implementation

Result:

The numerical difference between all three implementations is accurate up to:

6 decimal places

MAE and RMSE remain extremely small, confirming numerical consistency.

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📊 Visualization

The project generates:

• Time-domain comparison
• Difference curves
• Error metrics (MAE / RMSE)
• FFT spectrum comparison

All figures are automatically saved in the figures/ directory.

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🔬 Technical Specifications

• 4th-order Butterworth Bandpass Filter
• Sampling rate: 250 Hz
• Band: 4–40 Hz
• Optional 50 Hz notch filter
• Zero-phase forward-backward filtering
• Double precision floating-point implementation

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🎯 Application Scenarios

• EEG signal preprocessing
• Biomedical signal filtering
• Embedded DSP systems
• Real-time physiological monitoring devices

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🏁 Conclusion

This project demonstrates that:

A carefully designed pure C implementation can achieve nearly identical numerical precision to MATLAB and Python filtfilt().

It provides a reliable solution for deploying high-precision zero-phase filters in embedded systems.

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