{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:09:04Z","timestamp":1760231344183,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2022,9,7]],"date-time":"2022-09-07T00:00:00Z","timestamp":1662508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Autonomous University of Aguascalientes","award":["PII20-2"],"award-info":[{"award-number":["PII20-2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A frequency spectrum segmentation methodology is proposed to extract the frequency response of circuits and systems with high resolution and low distortion over a wide frequency range. A high resolution is achieved by implementing a modified Dirichlet function (MDF) configured for multi-tone excitation signals. Low distortion is attained by limiting or avoiding spectral leakage and interference into the frequency spectrum of interest. The use of a window function allowed for further reduction in distortion by suppressing system-induced oscillations that can cause severe interference while acquiring signals. This proposed segmentation methodology with the MDF generates an interleaved frequency spectrum segment that can be used to measure the frequency response of the system and can be represented in a Bode and Nyquist plot. The ability to simulate and measure the frequency response of the circuit and system without expensive network analyzers provides good stability coverage for reliable fault detection and failure avoidance. The proposed methodology is validated with both simulation and hardware.<\/jats:p>","DOI":"10.3390\/s22186757","type":"journal-article","created":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T04:18:32Z","timestamp":1662610712000},"page":"6757","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Interleaved Segmented Spectrum Analysis: A Measurement Technique for System Frequency Response and Fault Detection"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5532-362X","authenticated-orcid":false,"given":"Alejandro","family":"Roman-Loera","sequence":"first","affiliation":[{"name":"Department of Electronic Systems, Universidad Aut\u00f3noma de Aguascalientes, Aguascalientes 20100, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8431-3586","authenticated-orcid":false,"given":"Anurag","family":"Veerabathini","sequence":"additional","affiliation":[{"name":"Department of Electrical & Computer Engineering, New Mexico State University, Las Cruces, NM 88003, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7580-7533","authenticated-orcid":false,"given":"Jorge E.","family":"Macias-Diaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Didactics of Mathematics, School of Digital Technologies, Tallinn University, Narva Rd. 25, 10120 Tallinn, Estonia"},{"name":"Department of Mathematics and Physics, Universidad Aut\u00f3noma de Aguascalientes, Aguascalientes 20100, Mexico"}]},{"given":"Felipe de Jesus","family":"Rizo-Diaz","sequence":"additional","affiliation":[{"name":"Department of Electronic Systems, Universidad Aut\u00f3noma de Aguascalientes, Aguascalientes 20100, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Roman-Loera, A., Veerabathini, A., Oropeza, L.A.F., Mart\u00ednez, L.A.C., and Frias, D.M. (2021). Improved Frequency Compensation Technique for Three-Stage Amplifiers. J. Low Power Electron. Appl., 11.","DOI":"10.3390\/jlpea11010011"},{"key":"ref_2","unstructured":"(2022, August 25). Understanding Challenges in USB Charger Design for Automotive Applications, Application Note 7592. Maxim Integrated Products. Available online: https:\/\/www.maximintegrated.com\/en\/design\/technical-documents\/app-notes\/7\/7592.html."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Veerabathini, A., and Roman-Loera, A. (2022, January 7\u201310). A Peak Current-Mode Control Boost Converter Model for Stability Analysis: A Design Approach. Proceedings of the 2022 IEEE 65th International Midwest Symposium on Circuits and Systems (MWSCAS), Fukuoka, Japan.","DOI":"10.1109\/MWSCAS54063.2022.9859528"},{"key":"ref_4","unstructured":"Yao, H., Ning, X., Su, Y., Liu, X., and Jin, Z. (2013, January 24\u201325). A method for loop-circuit stability analysis. Proceedings of the 2013 International Workshop on Microwave and Millimeter Wave Circuits and System Technology, Chengdu, China."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1109\/TMTT.2017.2749222","article-title":"Model-Free Closed-Loop Stability Analysis: A Linear Functional Approach","volume":"66","author":"Cooman","year":"2018","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1109\/TMTT.2020.3036889","article-title":"Two-Level Stability Analysis of Complex Circuits","volume":"69","year":"2021","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ali, H., Zheng, X., Wu, X., Khan, S., and Saad, M. (2015, January 8\u201310). Frequency response measurements of DC-DC buck converter. Proceedings of the 2015 IEEE International Conference on Information and Automation, Lijiang, China.","DOI":"10.1109\/ICInfA.2015.7279658"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Fern\u00e1ndez, C., Zumel, P., Fern\u00e1ndez-Herrero, A., Sanz, M., L\u00e1zaro, A., and Barrado, A. (2011, January 6\u201311). Frequency response of switching DC\/DC converters from a single simulation in the time domain. Proceedings of the 2011 Twenty-Sixth Annual IEEE Applied Power Electronics Conference and Exposition (APEC), Fort Worth, TX, USA.","DOI":"10.1109\/APEC.2011.5744847"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1109\/63.76813","article-title":"A new, continuous-time model for current-mode control (power convertors)","volume":"6","author":"Ridley","year":"1991","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Faifer, M., Piegari, L., Rossi, M., and Toscani, S. (2021). An Average Model of DC\u2013DC Step-Up Converter Considering Switching Losses and Parasitic Elements. Energies, 14.","DOI":"10.3390\/en14227780"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Goyal, D., Chaturvedi, P., Nagar, A.K., and Purohit, S. (2021). Mathematical Modeling and Simulation of DC-DC Converters Using State-Space Approach. Proceedings of Second International Conference on Smart Energy and Communication. Algorithms for Intelligent Systems, Springer.","DOI":"10.1007\/978-981-15-6707-0"},{"key":"ref_12","unstructured":"Blaabjerg, F. (2018). Chapter 3\u2014Modeling and Control of DC-DC Converters. Control of Power Electronic Converters and Systems, Academic Press."},{"key":"ref_13","unstructured":"Liu, J., Yang, P., Lin, X., and Zhou, S. (2009, January 20\u201322). Modeling and simulation of DC\/DC converters based on double-loop control. Proceedings of the 2009 3rd International Conference on Power Electronics Systems and Applications (PESA), Hong Kong, China."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1109\/TPWRD.2019.2938020","article-title":"Estimating Power Transformer High Frequency Model Parameters Using Frequency Response Analysis","volume":"35","author":"Mosaad","year":"2020","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Alsuhaibani, S., Khan, Y., Beroual, A., and Malik, N.H. (2016). Review of Frequency Response Analysis Methods for Power Transformer Diagnostics. Energies, 9.","DOI":"10.3390\/en9110879"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Al-Ameri, S.M., Kamarudin, M.S., Yousof, M.F.M., Salem, A.A., Siada, A.A., and Mosaad, M.I. (2021). Interpretation of Frequency Response Analysis for Fault Detection in Power Transformers. Appl. Sci., 11.","DOI":"10.3390\/app11072923"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kornatowski, E., and Banaszak, S. (2020). Frequency Response Quality Index for Assessing the Mechanical Condition of Transformer Windings. Energies, 13.","DOI":"10.3390\/en13010029"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.ijepes.2012.03.004","article-title":"Sweep frequency response analysis for diagnosis of low level short circuit faults on the windings of power transformers: An experimental study","volume":"42","author":"Behjat","year":"2012","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"e2413","DOI":"10.1002\/etep.2413","article-title":"An induction motor model for system frequency response models","volume":"27","author":"Sigrist","year":"2017","journal-title":"Int. Trans. Electr. Energ Syst."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Sant\u2019Ana, W.C., Lambert-Torres, G., Bonaldi, E.L., Gama, B.R., Zacarias, T.G., Areias, I.A.d.S., Arantes, D.d.A., Assuncao, F.d.O., Campos, M.M., and Steiner, F.M. (2021). Online Frequency Response Analysis of Electric Machinery through an Active Coupling System Based on Power Electronics. Sensors, 21.","DOI":"10.3390\/s21238057"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Al-Ameri, S.M., Alawady, A.A., Yousof, M.F.M., Kamarudin, M.S., Salem, A.A., Abu-Siada, A., and Mosaad, M.I. (2022). Application of Frequency Response Analysis Method to Detect Short-Circuit Faults in Three-Phase Induction Motors. Appl. Sci., 12.","DOI":"10.3390\/app12042046"},{"key":"ref_22","unstructured":"Gavi\u00f1o, R. (2010). Introducci\u00f3n a Los Sistemas de Control: Conceptos, Aplicaciones y Simulaci\u00f3n con MATLAB, Pearson Education. [1st ed.]."},{"key":"ref_23","unstructured":"Ogata, K. (2010). Modern Control Engineering, Pearson Education. [5th ed.]."},{"key":"ref_24","unstructured":"Golnaraghi, F., and Kuo, B.C. (2009). Automatic Control Systems, Wiley Publishing. [9th ed.]."},{"key":"ref_25","unstructured":"Rajesh, S. (2011). A Cmos Mixed-Signal Magnitude and Phase Detector. [Master Thesis, New Mexico State University]."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2301","DOI":"10.1109\/JSSC.2006.881561","article-title":"An Integrated Frequency Response Characterization System With a Digital Interface for Analog Testing","volume":"41","author":"Hussien","year":"2006","journal-title":"IEEE J.-Solid-State Circuits"},{"key":"ref_27","unstructured":"Valdes-Garcia, A., Silva-Martinez, J., and Sanchez-Sinencio, E. (2004, January 25\u201329). An on-chip transfer function characterization system for analog built-in testing. Proceedings of the 22nd IEEE VLSI Test Symposium, Napa Valley, CA, USA."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2524","DOI":"10.1109\/TPEL.2008.2002066","article-title":"Integration of Frequency Response Measurement Capabilities in Digital Controllers for DC\u2013DC Converters","volume":"23","author":"Shirazi","year":"2008","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1109\/TPEL.2005.854035","article-title":"System identification of power converters with digital control through cross-correlation methods","volume":"20","author":"Miao","year":"2005","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_30","unstructured":"(2022, August 22). Sine Integral Function. Available online: https:\/\/la.mathworks.com\/help\/symbolic\/sinint.html."},{"key":"ref_31","unstructured":"Proakis, J.G., Manolakis, D.G., and Proakis, J.G. (1992). Digital Signal Processing: Principles, Algorithms, and Applications, Person Education. [4th ed.]."},{"key":"ref_32","unstructured":"Oppenheim, A.V., and Schafer, R.W. (2009). Discrete-Time Signal Processing, Prentice Hall Press. [3rd ed.]."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2898","DOI":"10.1038\/ncomms3898","article-title":"Optical sinc-shaped Nyquist pulses of exceptional quality","volume":"4","author":"Soto","year":"2013","journal-title":"Nat. Commun."},{"key":"ref_34","first-page":"7801411","article-title":"Combined Optical and Electrical Spectrum Shaping for High-Baud-Rate Nyquist-WDM Transceivers","volume":"8","author":"Borkowski","year":"2016","journal-title":"IEEE Photonics J."},{"key":"ref_35","unstructured":"(2022, July 02). Dirichlet or Periodic Sinc Function. Available online: https:\/\/la.mathworks.com\/help\/signal\/ref\/diric.html."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/18\/6757\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:24:52Z","timestamp":1760142292000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/18\/6757"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,7]]},"references-count":35,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["s22186757"],"URL":"https:\/\/doi.org\/10.3390\/s22186757","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,9,7]]}}}