# Using the Lomb-Scargle Periodogram for HRV analysis

While the HRV 2.0 Add-On has incorporated many changes at the user interface, there are some really important hidden improvements too - like the underlying algorithm. Here, we discuss the two most common frequency analysis algorithms used to study heart rate variability and explain why we've changed in HRV 2.0.

Frequency analysis of signals is a large and very technical field that can be traced back to the work of Joseph Fourier in the 19th century. Underpinning the field is the concept that any periodic signal can be decomposed into the sum of a number of discrete sinusoids without loss of information. In HRV analysis, frequency transforms are often used to produce a periodogram from the tachogram.

## The Fast Fourier Transform

Most programs, including HRV 1.4.2, typically use the Fast Fourier Transform (FFT) to produce a periodogram from the tachogram. However, the FFT is based on the assumption that all samples used in the analysis (i.e., all the RR intervals) are evenly spaced with time. Because the tachogram is not an evenly sampled signal, and the FFT algorithm is limited to dealing with evenly sampled signals, then some approximation is necessary. HRV 1.4.2 makes the approximation that the tachogram is evenly sampled and passes it directly to the FFT algorithm. This means that the sample interval of the tachogram is assumed to be equal to the average RR interval.

## The Lomb-Scargle Periodogram

HRV 2.0 uses the Lomb-Scargle Periodogram. This technique is based upon the same fundamental theory as the FFT but is superior in this context as it does not require an evenly sampled data set – it allows for the inherent variability of the RR interval data and hence the tachogram can be transformed directly without an intervening approximation stage. Unlike the FFT, the Lomb method also allows for the exclusion of ectopic beats without requiring an approximated beat to be put in its place as it is perfectly capable of dealing with gaps in the data set, giving you a more accurate analysis that is less affected by ectopic or missing beats.

"When considering the less-than-ideal inputs endemic to HRV studies, however, only the Lomb method produces robust PSD estimates in the presence of noise and ectopy. The Lomb method avoids all of the complications and pitfalls of resampling and replacement of outliers, and introduces no drawbacks of its own; in consequence, it is the method of choice for PSD estimation of heart rate."

Moody GB. "Spectral Analysis of Heart Rate Without Resampling" Computers in Cardiology 1993. IEEE Computer Society Press, vol 20; 715-718

We thought this was a really important change to make in the HRV 2.0 Add-On. We hope you think so too!