Fractal filtering of channel data

Area of Science:

• Signal Processing
• Time Series Analysis
• Data Filtering Techniques

Background:

• Time series data often contains noise that can obscure important features.
• Traditional filtering methods may attenuate significant signal transients.
• Fractal dimension offers a novel metric for characterizing data complexity.

Purpose of the Study:

• To introduce and evaluate a fractal filtering method for time series data.
• To demonstrate the effectiveness of fractal filtering in noise reduction while preserving signal features.
• To compare different functions for modulating filter parameters based on fractal dimension.

Main Methods:

• Calculated the fractal dimension (D) for subsets of time series data.
• Employed a recursive filter with a weighting factor (w) adjusted by D.
• Investigated linear and ogive functions to modify the weighting factor w.
• Utilized the ogive function w = [1 + p(1.5-D)]-1 for noise removal.

Main Results:

• Fractal filtering successfully reduced baseline noise in time series data.
• Large transient shifts in baseline were retained with minimal amplitude decrease.
• The ogive function proved most effective for noise removal while preserving opening/closing events.
• The method is applicable to single-channel data with flickering and numerous events.

Conclusions:

• Fractal dimension provides a valuable parameter for adaptive data filtering.
• The proposed fractal filtering technique offers superior noise reduction compared to traditional methods.
• This approach enhances the analysis of time series data, particularly in applications with transient events.