A novel recursive Fourier transform for nonuniform sampled signals: application to heart rate variability spectrum...

Area of Science:

• Signal Processing
• Biomedical Engineering
• Time Series Analysis

Background:

• Non-uniform sampling presents challenges in signal analysis, particularly for physiological data like heart rate variability (HRV).
• Traditional methods for power spectral density (PSD) estimation often require uniform sampling or involve computationally intensive algorithms.

Purpose of the Study:

• To introduce a novel Recursive Fourier Transform (RFT) for efficiently calculating discrete Fourier transforms of non-uniformly sampled time series.
• To evaluate the RFT's efficacy for power spectral density (PSD) estimation in heart rate variability (HRV) analysis, comparing it against the Lomb-Scargle Transform (LST).

Main Methods:

• The Recursive Fourier Transform (RFT) iteratively computes discrete Fourier transforms without requiring sample interpolation to uniform time intervals.
• The RFT achieves a computational order of N for N frequencies, offering significant efficiency gains.
• The study involved analyzing quasi-stationary signals with simulated missing heartbeats to assess estimation performance.

Main Results:

• The RFT demonstrated comparable estimation performance to the Lomb-Scargle Transform (LST) for PSD estimation of HRV.
• The RFT exhibited significantly lower computational overhead and complexity compared to the LST.
• The RFT is particularly well-suited for iterative spectrum estimation applications with non-uniform time samples.

Conclusions:

• The Recursive Fourier Transform (RFT) provides an efficient and effective alternative for power spectral density estimation of non-uniformly sampled data, especially in heart rate variability analysis.
• The RFT's computational efficiency makes it a valuable tool for real-time or resource-constrained applications.
• This novel method addresses key limitations of existing techniques for analyzing irregular time series data.