Instantaneous Frequencies of Continuous Blood Pressure a Comparison of the Power Spectrum, the Continuous Wavelet Transform and the Hilbert–Huang Transform

Kathrine Knai,Geir Kulia,Nils Kristian Skjaervold,Marta Molinas

doi:10.1142/s2424922x17500097

Abstract

Continuous biological signals, like blood pressure recordings, exhibit nonlinear and nonstationary properties which must be considered during their analysis. Heart rate variability analyses have identified several frequency components and their autonomic origin. There is need for more knowledge on the time-changing properties of these frequencies. The power spectrum, continuous wavelet transform and Hilbert–Huang transform are applied on a continuous blood pressure signal to investigate how the different methods compare to each other. The Hilbert–Huang transform shows high ability to analyze such data, and can, by identifying instantaneous frequency shifts, provide new insights into the nature of these kinds of data.

Highlights

Continuous biological signals, like blood pressure recordings, exhibit both nonlinear and nonstationary properties which must be considered during their analysis [Usui and Toda (1991)]
We see that areas with high power in the continuous wavelet transform (CWT) only partially correspond to areas with high power in the Hilbert spectrum. We suggest that this is caused by poor resolution of the CWT and removal of Intrinsic Mode Functions (IMFs) that would have blocked the view of the CWT
The Power spectrum differs from CWT and Hilbert–Huang Transform (HHT) as it shows the frequency distribution in the signal under the assumption of time invariant amplitude and frequency values

Summary

Background

Continuous biological signals, like blood pressure recordings, exhibit both nonlinear and nonstationary properties which must be considered during their analysis [Usui and Toda (1991)]. The Hilbert–Huang Transform (HHT) was introduced in 1998 by Norden Huang [Huang et al (1998)] It was originally developed for analyzing nonstationary ocean waves and is, unlike the aforementioned methods, not based on the Fourier Transform. The regulatory origin of these components have been studied to a great extent [Shaffer et al (2014); Li et al (2011)], but there is a need for more knowledge on the time-changing properties of these frequencies and the transferability to other biological signals, such as blood pressure. The power spectrum, CWT, and HHT are applied on a real-life continuous blood pressure signal to investigate how the different methods compare to each other in terms of instantaneous frequency capture, focusing on the LF and VLF-range. The ULF are only identifiable in recordings longer than 5 min and beyond the scope of this paper

Study Material

Results

Hilbert–Huang transform

Comparison of the methods

Methodological considerations