i-RheoFT: Fourier transforming sampled functions without artefacts

Area of Science:

• Computational Physics
• Rheology
• Data Analysis

Background:

• Fourier transforms are crucial for analyzing time-dependent functions in various scientific fields.
• Accurate Fourier transform evaluation requires careful consideration of sampled data limitations and interpolation methods.
• Existing methods may struggle with unequally spaced, finite datasets and noise.

Purpose of the Study:

• To present and validate the new open-access code, i-RheoFT, for calculating Fourier transforms.
• To investigate the impact of experimental factors like data point density, interpolation, and noise on Fourier transform accuracy.
• To provide a reliable tool for analyzing discrete, time-averaged functions in rheology and related fields.

Main Methods:

• Implementation of an analytical method for Fourier transforms of generic time-dependent functions.
• Employment of i-RheoFT to analyze the effects of initial data point density, interpolation functions (Spline, Makima, PCHIP), and signal-to-noise ratio.
• Systematic evaluation of interpolation performance under varying data quality and density.

Main Results:

• i-RheoFT accurately computes Fourier transforms for sampled functions, even with unequally spaced data.
• At high signal-to-noise ratios and data density, Spline interpolation generally performs best.
• Performance degrades significantly below certain thresholds of data density or signal-to-noise ratio, with PCHIP and Makima showing better resilience in specific low-quality scenarios.

Conclusions:

• i-RheoFT offers a robust solution for Fourier transform calculations on experimental data.
• The choice of interpolation method is critical and depends on data quality and density.
• The code is valuable for researchers analyzing dynamics from discrete, time-averaged functions in rheology and beyond.