An efficient time-varying filter for detrending and bandwidth limiting the heart rate variability tachogram without resampling: MATLAB open-source code and Internet web-based implementation

Abstract

The heart rate variability (HRV) signal derived from the ECG is a beat-to-beat record of RR intervals and is, as a time series, irregularly sampled. It is common engineering practice to resample this record, typically at 4 Hz, onto a regular time axis for analysis in advance of time domain filtering and spectral analysis based on the DFT. However, it is recognised that resampling introduces noise and frequency bias. The present work describes the implementation of a time-varying filter using a smoothing priors approach based on a Gaussian process model, which does not require data to be regular in time. Its output is directly compatible with the Lomb-Scargle algorithm for power density estimation. A web-based demonstration is available over the Internet for exemplar data. The MATLAB (MathWorks Inc.) code can be downloaded as open source.

Figure 1

Weight functions (viz. D ₂ operator).

Figure 2

Bode plot of theoretical transfer function of equivalent kernel filter.

Figure 3

Bode plot of discrete transfer function of equivalent kernel filter.

Figure 4

Synthetic and clinical HRV records band-pass filtered by sequential application of SGP: raw data vt ₀ “smoothed” to give vt ₁; vt ₂ = vt ₀ − vt ₁ (not shown); vt ₂ “smoothed” to give vt ₃. Lomb Scargle Periodograms (LSPs) are for vt ₀, vt ₂, and vt ₃.

Figure 5

Speed-up of SGP over SPA with increasing data set size.