Detrended Fluctuation Analysis (DFA) Implementation

Overview

This project implements Detrended Fluctuation Analysis (DFA), a method for scaling analysis in non-stationary time series data. The project includes pre-processing ECG signals, removing noise, and analyzing fractal properties using DFA.

Features

• Signal Pre-processing:
  • Removes powerline interference using a notch filter.
  • Smooths the signal with wavelet decomposition.
• DFA Implementation:
  • Computes scaling exponents to detect long-range correlations.
  • Provides visualization for easier interpretation of results.
• Visualization:
  • Plots raw, filtered, and detrended data.
  • Generates DFA log-log plots to analyze scaling properties.

Project Files

1. DFA.m:

   • Contains the DFA algorithm.
   • Inputs:
     • DATA: Input time-series data.
     • win_length: Window length for segmenting the data.
     • order: Polynomial order for detrending.
   • Outputs:
     • sum1: Fluctuation measure.
     • y: Integrated signal.
     • y_n: Polynomial-detrended signal.
     • N1: Effective data length.

2. DFA_call_p.m:

   • Performs pre-processing and calls the DFA function.
   • Steps:
     1. Removes powerline noise from the ECG signal.
     2. Decomposes the signal using wavelets and smooths it.
     3. Runs DFA for various window lengths and visualizes results.
   • Outputs: Visualized steps of the processing and calculated DFA slopes.

Prerequisites

• MATLAB or compatible environment.
• Required Toolboxes:
  • Signal Processing Toolbox.
  • Wavelet Toolbox.

Outputs

• Filtered Signal: Displays the denoised ECG signal.
• DFA Results:
  • Log-log plot showing fluctuation function $F(n)$ vs. window size $n$.
  • Slope of the log-log plot ($alpha$) representing scaling properties.
  • Fractal dimension $D$ derived as $D$ = $3$ - $alpha$.

Key Visualizations

1. Raw ECG Signal: Plotted before filtering.
2. Filtered Signal: After noise removal and smoothing.
3. DFA Signal Fitting:
   • Integrated series $y(n)$ and detrended signal $y_n(n)$.
4. Log-Log Plot:
   • Displays the relationship between $F(n)$ and $n$ with computed slopes.

References

• Peng, C.-K., et al. "Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series", Physical Review E, 1995.

Author

[Dimitris Charistes, Dimitris Bismpas]