{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T02:24:45Z","timestamp":1774923885171,"version":"3.50.1"},"reference-count":52,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T00:00:00Z","timestamp":1680825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science and Technology Council, Taiwan","award":["NSTC 110-2221-E-035-006-MY3"],"award-info":[{"award-number":["NSTC 110-2221-E-035-006-MY3"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Frequency estimation plays a critical role in vital sign monitoring. Methods based on Fourier transform and eigen-analysis are commonly adopted techniques for frequency estimation. Because of the nonstationary and time-varying characteristics of physiological processes, time-frequency analysis (TFA) is a feasible way to perform biomedical signal analysis. Among miscellaneous approaches, Hilbert\u2013Huang transform (HHT) has been demonstrated to be a potential tool in biomedical applications. However, the problems of mode mixing, unnecessary redundant decomposition and boundary effect are the common deficits that occur during the procedure of empirical mode decomposition (EMD) or ensemble empirical mode decomposition (EEMD). The Gaussian average filtering decomposition (GAFD) technique has been shown to be appropriate in several biomedical scenarios and can be an alternative to EMD and EEMD. This research proposes the combination of GAFD and Hilbert transform that is termed the Hilbert\u2013Gauss transform (HGT) to overcome the conventional drawbacks of HHT in TFA and frequency estimation. This new method is verified to be effective for the estimation of respiratory rate (RR) in finger photoplethysmography (PPG), wrist PPG and seismocardiogram (SCG). Compared with the ground truth values, the estimated RRs are evaluated to be of excellent reliability by intraclass correlation coefficient (ICC) and to be of high agreement by Bland\u2013Altman analysis.<\/jats:p>","DOI":"10.3390\/s23083785","type":"journal-article","created":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T04:04:16Z","timestamp":1680840256000},"page":"3785","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Frequency Estimation Scheme Based on Gaussian Average Filtering Decomposition and Hilbert Transform: With Estimation of Respiratory Rate as an Example"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1495-166X","authenticated-orcid":false,"given":"Yue-Der","family":"Lin","sequence":"first","affiliation":[{"name":"Department of Automatic Control Engineering, Feng Chia University, Taichung 40724, Taiwan"},{"name":"Ph.D. Program of Electrical and Communications Engineering, Feng Chia University, Taichung 40724, Taiwan"}]},{"given":"Yong-Kok","family":"Tan","sequence":"additional","affiliation":[{"name":"Ph.D. Program of Electrical and Communications Engineering, Feng Chia University, Taichung 40724, Taiwan"}]},{"given":"Tienhsiung","family":"Ku","sequence":"additional","affiliation":[{"name":"Department of Anesthesiology, Changhua Christian Hospital, Changhua 50051, Taiwan"},{"name":"Artificial Intelligence Development Center, Changhua Christian Hospital, Changhua 50051, Taiwan"}]},{"given":"Baofeng","family":"Tian","sequence":"additional","affiliation":[{"name":"College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130061, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1001\/jama.1980.03310100041029","article-title":"Respiratory rate as an indicator of acute respiratory dysfunction","volume":"244","author":"Gravelyn","year":"1980","journal-title":"JAMA"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1136\/bmj.284.6316.626","article-title":"Raised respiratory rate in elderly patients: A valuable physical sign","volume":"284","author":"McFadden","year":"1982","journal-title":"Br. Med. J. (Clin. Res. Ed.)"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1007\/BF02600071","article-title":"Respiratory rate predicts cardiopulmonary arrest for internal medicine inpatients","volume":"8","author":"Fieselmann","year":"1993","journal-title":"J. Gen. Intern. Med."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"12","DOI":"10.7748\/en2011.05.19.2.12.c8504","article-title":"Rate of respiration: The forgotten vital sign","volume":"19","author":"Parkes","year":"2011","journal-title":"Emerg. Nurse"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Miller, D.J., Capodilupo, J.V., Lastella, M., Sargent, C., Roach, G.D., Lee, V.H., and Capodilupo, E.R. (2020). Analyzing changes in respiratory rate to predict the risk of COVID-19 infection. PLoS ONE, 15.","DOI":"10.1101\/2020.06.18.20131417"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Nicol\u00f2, A., Massaroni, C., Schena, E., and Sacchetti, M. (2020). The importance of respiratory rate monitoring: From healthcare to sport and exercise. Sensors, 20.","DOI":"10.3390\/s20216396"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1152\/jappl.1964.19.1.166","article-title":"Volumetric dynamics of respiration as measured by electrical impedance plethysmography","volume":"19","author":"Allison","year":"1964","journal-title":"J. Appl. Physiol."},{"key":"ref_8","first-page":"113","article-title":"Derivation of respiratory signals from multi-lead ECGs","volume":"12","author":"Moody","year":"1985","journal-title":"Comput. Cardiol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1088\/0967-3334\/37\/9\/1573","article-title":"Real-time multi-signal frequency tracking with a bank of notch filters to estimate the respiratory rate from the ECG","volume":"37","author":"Mirmohamadsadeghi","year":"2016","journal-title":"Physiol. Meas."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF01641813","article-title":"Capnometers","volume":"4","author":"Rantala","year":"1988","journal-title":"J. Clin. Monit."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1093\/bja\/67.3.341","article-title":"Aura: A new respiratory monitor and apnoea alarm for spontaneously breathing patients","volume":"67","author":"Cyna","year":"1991","journal-title":"Br. J. Anaesth."},{"key":"ref_12","first-page":"232","article-title":"Human body respiration measurement using digital temperature sensor with I2C interface","volume":"4","author":"Agnihotri","year":"2013","journal-title":"Int. J. Electron. Commun. Comput. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.bspc.2017.03.009","article-title":"Wavelet-based embedded algorithm for respiratory rate estimation from PPG signal","volume":"36","author":"Lin","year":"2017","journal-title":"Biomed. Signal Process. Control."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41746-019-0083-3","article-title":"Respiration rate and volume measurements using wearable strain sensors","volume":"2","author":"Chu","year":"2019","journal-title":"NPJ Digit. Med."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"101779","DOI":"10.1016\/j.bspc.2019.101779","article-title":"Estimation of heart rate and respiratory rate from the seismocardiogram under resting state","volume":"57","author":"Lin","year":"2020","journal-title":"Biomed. Signal Process. Control."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4350","DOI":"10.1109\/JSEN.2020.3033047","article-title":"Developing conductive fabric threads for human respiratory rate monitoring","volume":"21","author":"Ali","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"07TR01","DOI":"10.1088\/1361-6579\/ab299e","article-title":"Recent development of respiratory rate measurement technologies","volume":"40","author":"Liu","year":"2019","journal-title":"Physiol. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Vanegas, E., Igual, R., and Plaza, I. (2020). Sensing systems for respiration monitoring: A technical systematic review. Sensors, 20.","DOI":"10.3390\/s20185446"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1114","DOI":"10.1049\/iet-spr.2016.0702","article-title":"Novel subspace method for frequencies estimation of two sinusoids with applications to vital signals","volume":"11","author":"Chen","year":"2017","journal-title":"IET Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1109\/LSP.2011.2136378","article-title":"A method for fine resolution frequency estimation from three DFT samples","volume":"18","author":"Candan","year":"2011","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_21","unstructured":"Marple, S.L. (1987). Digital Spectral Analysis with Applications, Prentice Hall."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3837","DOI":"10.1109\/TSP.2008.924856","article-title":"Quantitative performance analysis of scalogram as instantaneous frequency estimator","volume":"56","author":"Sejdic","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"124022","DOI":"10.1103\/PhysRevD.79.124022","article-title":"Methods for detection and characterization of signals in noisy data with the Hilbert-Huang transform","volume":"79","author":"Stroeer","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Rangayyan, R.M. (2015). Biomedical Signal Analysis, John Wiley & Sons. [2nd ed.].","DOI":"10.1002\/9781119068129"},{"key":"ref_25","unstructured":"Hayes, M.H. (1996). Statistical Digital Signal Processing and Modeling, John Wiley & Sons."},{"key":"ref_26","first-page":"232","article-title":"A comparison of signal processing techniques for the extraction of breathing rate from the photoplethysmogram","volume":"2","author":"Fleming","year":"2007","journal-title":"Int. J. Biol. Med. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2054","DOI":"10.1109\/TBME.2009.2019766","article-title":"Estimation of respiratory rate from photoplethysmogram data using time-frequency spectral estimation","volume":"56","author":"Chon","year":"2009","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S1793536909000047","article-title":"Ensemble empirical mode decomposition: A noise-assisted data analysis method","volume":"1","author":"Wu","year":"2009","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Huang, N.E., and Shen, S.S.P. (2014). Hilbert-Huang Transform and Its Applications, World Scientific.","DOI":"10.1142\/8804"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.bspc.2006.02.001","article-title":"Time-frequency analysis of normal and abnormal biological signals","volume":"1","author":"Mahmoud","year":"2006","journal-title":"Biomed. Signal Process. Control."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Na\u00eft-Ali, A. (2009). Advanced Biosignal Processing, Springer.","DOI":"10.1007\/978-3-540-89506-0"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Laskovski, A. (2011). Biomedical Engineering, Trends in Electronics, Communications and Software, IntechOpen.","DOI":"10.5772\/549"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"103292","DOI":"10.1016\/j.dsp.2021.103292","article-title":"A survey on Hilbert-Huang transform: Evolution, challenges and solutions","volume":"120","author":"Escola","year":"2022","journal-title":"Digit. Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"103104","DOI":"10.1016\/j.bspc.2021.103104","article-title":"A novel approach for decomposition of biomedical signals in different applications based on data-adaptive Gaussian average filtering","volume":"71","author":"Lin","year":"2022","journal-title":"Biomed. Signal Process. Control."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.aenj.2016.12.003","article-title":"Accurate respiratory rates count: So should you!","volume":"20","author":"Flenady","year":"2017","journal-title":"Australas. Emerg. Nurs. J."},{"key":"ref_37","unstructured":"Fisher, R. (1925). Statistical Methods for Research Worker, Oliver & Boyd."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1037\/1082-989X.1.1.30","article-title":"Forming inferences about some intraclass correlation coefficients","volume":"1","author":"McGraw","year":"1996","journal-title":"Psychol. Methods"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/S0140-6736(86)90837-8","article-title":"Statistical methods for assessing agreement between two methods of clinical measurement","volume":"1","author":"Bland","year":"1986","journal-title":"Lancet"},{"key":"ref_40","unstructured":"Moody, G.B., and Mark, R.G. (1996, January 8\u201311). A database to support development and evaluation of intelligent intensive care monitoring. Proceedings of the Computers in Cardiology 1996, Indianapolis, IN, USA."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"e215","DOI":"10.1161\/01.CIR.101.23.e215","article-title":"PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals","volume":"101","author":"Goldberger","year":"2000","journal-title":"Circulation"},{"key":"ref_42","unstructured":"(2023, February 01). PhysioNet LightWAVE. Available online: https:\/\/archive.physionet.org\/lightwave\/."},{"key":"ref_43","unstructured":"Garc\u00eda-Gonz\u00e1lez, M.A., Argelag\u00f3s-Palau, A., Fern\u00e1ndez-Chimeno, M., and Ramos-Castro, J. (2013, January 22\u201325). A comparison of heartbeat detectors for the seismocardiogram. Proceedings of the Computing in Cardiology 2013, Zaragoza, Spain."},{"key":"ref_44","unstructured":"Lin, Y.D. (2023, February 01). Python Code for Gaussian Average Fltering Decomposition (GAFD). Available online: https:\/\/github.com\/yudlin\/GAFD."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2977","DOI":"10.21105\/joss.02977","article-title":"EMD: Empirical mode decomposition and Hilbert-Huang spectral analyses in Python","volume":"6","author":"Quinn","year":"2021","journal-title":"J. Open Source Softw."},{"key":"ref_46","unstructured":"Lin, Y.D. (2023, February 01). Python Code for Bland-Altman\u2019s Agreement Analysis. Available online: https:\/\/github.com\/yudlin\/Agreement_Analysis."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.21105\/joss.01237","article-title":"PyWavelets: A Python package for wavelet analysis","volume":"4","author":"Lee","year":"2019","journal-title":"J. Open Source Softw."},{"key":"ref_48","unstructured":"Lin, Y.D. (2023, February 01). Python Code for Complex Morlet Wavelet. Available online: https:\/\/github.com\/yudlin\/wavePSD."},{"key":"ref_49","unstructured":"Salarian, A., and Intraclass Correlation Coefficient (ICC) (2023, February 01). MATLAB Central File Exchange. Available online: https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/22099-intraclass-correlation-coefficient-icc."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1109\/PROC.1978.10837","article-title":"On the use of windows for harmonic analysis with the discrete Fourier transform","volume":"66","author":"Harris","year":"1978","journal-title":"Proc. IEEE"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1142\/S179353690900028X","article-title":"Iterative filtering as an alternative algorithm for empirical mode decomposition","volume":"1","author":"Lin","year":"2009","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.jcm.2016.02.012","article-title":"A guideline of selecting and reporting intraclass correlation coefficients for reliability research","volume":"15","author":"Koo","year":"2016","journal-title":"J. Chiropr. Med."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/8\/3785\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:11:45Z","timestamp":1760123505000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/8\/3785"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,7]]},"references-count":52,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["s23083785"],"URL":"https:\/\/doi.org\/10.3390\/s23083785","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,7]]}}}