{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T17:30:31Z","timestamp":1778866231092,"version":"3.51.4"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T00:00:00Z","timestamp":1743984000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT\/MECI through national funds and when applicable co-funded EU funds","award":["UID\/50008"],"award-info":[{"award-number":["UID\/50008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sci"],"abstract":"<jats:p>Estimating the amplitude of a sinewave from a set of data points is a common procedure in various applications. This is typically achieved using a least squares method that provides closed-form estimators. The sampling process itself is often affected by different non-ideal phenomena like additive noise, phase noise, or sampling jitter, for example. Here, the precision of the estimation of a sinewave amplitude when the samples are affected by phase noise or sampling jitter is studied in the case of coherent sampling. The mathematical expression derived is useful in obtaining the confidence intervals for the estimated sinusoidal amplitude. It is also valuable at the time of choosing the proper number of samples to acquire from a signal in order to reach a certain desired level of sinewave amplitude estimation precision. The analytical expression presented is validated using both numerically generated data and experimental data. Various non-ideal factors, such as a fixed, uncontrollable amount of jitter in the setup, additive noise, analog-to-digital converter non-linearity, and limited signal bandwidth, are observed and discussed. Additionally, this work presents an exhaustive overview of the technical aspects involved in the experimental validation, including the implementation of the Monte Carlo type procedure, instrument interface, programming language, and the general development of automated measurement systems, which may be useful to other engineers.<\/jats:p>","DOI":"10.3390\/sci7020044","type":"journal-article","created":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T05:59:00Z","timestamp":1744091940000},"page":"44","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Contribution of Jitter and Phase Noise to the Precision of Sinusoidal Amplitude Estimation Using Coherent Sampling"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0854-489X","authenticated-orcid":false,"given":"Francisco A. C.","family":"Alegria","sequence":"first","affiliation":[{"name":"Instituto Superior T\u00e9cnico, University of Lisbon and Instituto de Telecomunica\u00e7\u00f5es, Av. Rovisco Pais, 1, Torre Norte, Piso 10, 1049-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,7]]},"reference":[{"key":"ref_1","unstructured":"Rao, S.S. (2004). Mechanical Vibrations, Prentice Hall. [4th ed.]."},{"key":"ref_2","unstructured":"Kramer, S.L. (1996). Geotechnical Earthquake Engineering, Prentice Hall."},{"key":"ref_3","unstructured":"Dally, J.W., Riley, W.F., and McConnell, K.G. (1993). Instrumentation for Engineering Measurements, John Wiley & Sons. [2nd ed.]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.ultras.2015.06.018","article-title":"A Multi-Frequency Method for Ultrasonic Ranging","volume":"63","author":"Alegria","year":"2015","journal-title":"Ultrasonics"},{"key":"ref_5","unstructured":"Kay, S.M. (1993). Fundamentals of Statistical Signal Processing, Volume I: Estimation, Pearson. [1st ed.]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1109\/TIM.2013.2282220","article-title":"A Rigorous Analysis of Least Squares Sine Fitting Using Quantized Data: The Random Phase Case","volume":"63","author":"Carbone","year":"2014","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_7","unstructured":"Stoica, P., and Moses, R.L. (2005). Spectral Analysis of Signals, Prentice Hall."},{"key":"ref_8","first-page":"1189","article-title":"Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm","volume":"49","year":"2001","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.isatra.2011.10.003","article-title":"Analytical Metrological Characterization of the Three-Parameter Sine Fit Algorithm","volume":"51","author":"Martino","year":"2012","journal-title":"ISA Trans."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.measurement.2019.05.047","article-title":"Review on jitter terminology and definitions","volume":"145","author":"Balestrieri","year":"2019","journal-title":"Measurement"},{"key":"ref_11","unstructured":"Reinhardt, V.S. (2005, January 29\u201331). A Review of Time Jitter and Digital Systems. Proceedings of the 2005 IEEE International Frequency and Control Symposium and Exposition, Vancouver, BC, Canada."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1109\/TIM.1987.6312595","article-title":"Effect of Quantization Errors on Some Periodic Signal Measurements","volume":"36","author":"Wagdy","year":"1987","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1109\/19.50422","article-title":"Effect of Sampling Jitter on Some Sine Wave Measurements","volume":"39","author":"Wagdy","year":"1990","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_14","unstructured":"Shize, G., Chunming, L., and Shenghe, S. (1994, January 10\u201312). The Effect of Sampling Noise on Band limited Periodic Signal Measurement. Proceedings of the Instrumentation and Measurement Technology Conference, Hamamatsu, Japan."},{"key":"ref_15","first-page":"465","article-title":"Contribution of Jitter to the Error of Amplitude Estimation of a Sinusoidal Signal","volume":"XVI","author":"Alegria","year":"2009","journal-title":"Metrol. Meas. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2328","DOI":"10.1109\/TIM.2009.2034576","article-title":"Gaussian Jitter-Induced Bias of Sine Wave Amplitude Estimation Using Three-Parameter Sine Fitting","volume":"59","author":"Alegria","year":"2010","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"107116","DOI":"10.1016\/j.jfranklin.2024.107116","article-title":"Uncertainty of the initial phase estimation of a sinewave in the presence of phase noise, additive noise or jitter","volume":"361","author":"Alegria","year":"2024","journal-title":"J. Frankl. Inst."},{"key":"ref_18","unstructured":"Papoulis, A. (1991). Probability, Random Variables and Stochastic Processes, McGraw-Hill. [3rd ed.]."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Alegria, F.C., Xie, L., and Pasadas, D. (2024). Study of the Bias of the Initial Phase Estimation of a Sinewave of Known Frequency in the Presence of Phase Noise. Sensors, 24.","DOI":"10.3390\/s24123730"},{"key":"ref_20","unstructured":"(2018). EEE Standard for Ethernet (Standard No. IEEE Standard 802.3-2018)."},{"key":"ref_21","unstructured":"PCI-SIG (2002). PCI Express Base Specification Revision 3.0, PCI-SIG."},{"key":"ref_22","unstructured":"Pohlmann, K.C. (2010). Principles of Digital Audio, McGraw-Hill. [6th ed.]."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Razavi, B. (1995). Principles of Data Conversion System Design, Wiley-IEEE Press.","DOI":"10.1109\/9780470545638"},{"key":"ref_24","unstructured":"Pratap, M., and Enge, P. (2006). Global Positioning System: Signals, Measurements, and Performance, Ganga-Jamuna Press."},{"key":"ref_25","unstructured":"(2013). HDMI 2.0 Specification, HDMI Forum, Inc.. HDMI Forum Technical Working Group."},{"key":"ref_26","unstructured":"(2018). Base Station (BS) Radio Transmission and Reception (Standard No. 3GPP TS 38.104, NR)."},{"key":"ref_27","unstructured":"(2018). IEEE Standard for Digitizing Waveform Recorders in IEEE Std 1057-2017 (Revision of IEEE Std 1057-2007) (Standard No. IEEE Std 1057-2017)."}],"container-title":["Sci"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2413-4155\/7\/2\/44\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:11:30Z","timestamp":1760029890000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2413-4155\/7\/2\/44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,7]]},"references-count":27,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["sci7020044"],"URL":"https:\/\/doi.org\/10.3390\/sci7020044","relation":{},"ISSN":["2413-4155"],"issn-type":[{"value":"2413-4155","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,7]]}}}