IOP PUBLISHING PHYSIOLOGICAL MEASUREMENT Physiol. Meas. 30 (2009) 43–61 doi:10.1088/0967-3334/30/1/004 Spectral analysis of time series of events: effect of respiration on heart rate in neonates Wim van Drongelen 1,3 , Amber L Williams 2 and Robert E Lasky 2 1 Department of Pediatrics, The University of Chicago, Chicago, IL 60637-1470, USA 2 Center for Clinical Research and Evidence-Based Medicine, The University of Texas–Houston Medical School, Houston, TX 77030, USA E-mail: wvandron@peds.bsd.uchicago.edu Received 6 May 2008, accepted for publication 18 November 2008 Published 15 December 2008 Online at stacks.iop.org/PM/30/43 Abstract Certain types of biomedical processes such as the heart rate generator can be considered as signals that are sampled by the occurring events, i.e. QRS complexes. This sampling property generates problems for the evaluation of spectral parameters of such signals. First, the irregular occurrence of heart beats creates an unevenly sampled data set which must either be pre-processed (e.g. by using trace binning or interpolation) prior to spectral analysis, or analyzed with specialized methods (e.g. Lomb’s algorithm). Second, the average occurrence of events determines the Nyquist limit for the sampled time series. Here we evaluate different types of spectral analysis of recordings of neonatal heart rate. Coupling between respiration and heart rate and the detection of heart rate itself are emphasized. We examine both standard and data adaptive frequency bands of heart rate signals generated by models of coupled oscillators and recorded data sets from neonates. We find that an important spectral artifact occurs due to a mirror effect around the Nyquist limit of half the average heart rate. Further we conclude that the presence of respiratory coupling can only be detected under low noise conditions and if a data-adaptive respiratory band is used. Keywords: cardiovascular system, pediatrics, signal processing, high- frequency band 1. Introduction Spectral analysis is a powerful tool for the analysis of biomedical signals. Current instrumentation samples and stores time series efficiently and at reasonable cost to allow 3 Author to whom any correspondence should be addressed. 0967-3334/09/010043+19$30.00 © 2009 Institute of Physics and Engineering in Medicine Printed in the UK 43