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The proposed estimator leverages a dichotomous search process before iterative interpolation estimation, which significantly reduces computational complexity while maintaining high estimation accuracy. An in-depth exploration of the relationship between the optimal parameter p and the unknown parameter \u03b4 forms the backbone of the methodology. Through extensive simulations and real-world experiments, the Ds-IpDTFT estimator exhibits superior performance relative to other established estimators, demonstrating robustness in noisy conditions and stability across varying frequencies. This efficient and accurate estimation method is a significant contribution to the field of signal processing and offers promising potential for practical applications.<\/jats:p>","DOI":"10.3390\/s23177461","type":"journal-article","created":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T06:10:22Z","timestamp":1693203022000},"page":"7461","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Performance Optimization in Frequency Estimation of Noisy Signals: Ds-IpDTFT Estimator"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1182-4035","authenticated-orcid":false,"given":"Miaomiao","family":"Wei","sequence":"first","affiliation":[{"name":"Department of Electronic and Information, Zhongyuan University of Technology, Zhengzhou 450007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongsheng","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Electronic and Information, Zhongyuan University of Technology, Zhengzhou 450007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Electronic and Information, Zhongyuan University of Technology, Zhengzhou 450007, China"},{"name":"Department of Information Engineering, Zhengzhou University, Zhengzhou 450001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiangyang","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Electronic and Information, Zhongyuan University of Technology, Zhengzhou 450007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaomin","family":"Mu","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Zhengzhou University, Zhengzhou 450001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9341-5077","authenticated-orcid":false,"given":"Juncai","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Case Western Reserve University, Cleveland, OH 44106, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1109\/TPWRD.2015.2418778","article-title":"A Complex Least Squares Enhanced Smart DFT Technique for Power System Frequency Estimation","volume":"32","author":"Xia","year":"2017","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"5163","DOI":"10.1109\/TSG.2017.2682098","article-title":"Power System Frequency Estimation of Sine-Wave Corrupted with Noise by Windowed Three-Point Interpolated DFT","volume":"9","author":"Wen","year":"2018","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1614","DOI":"10.1109\/TII.2020.2998096","article-title":"Frequency Estimation in Interpolated Discrete Fourier Transform with Generalized Maximum Sidelobe Decay Windows for the Control of Power","volume":"17","author":"Borkowski","year":"2021","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Hao, W., Cui, X., Feng, J., Dong, G., and Zhu, Z. (2018). Direct Instantaneous Frequency Rate Estimation to Improve the Carrier Estimation Performance in Mars Entry, Descent, and Landing Flight. Remote Sens., 10.","DOI":"10.3390\/rs10081259"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wang, J., Jiang, C., Kuang, L., and Guo, S. (2020, January 15\u201319). Iterative Doppler Frequency Offset Estimation in Low SNR Satellite Communications. Proceedings of the 2020 International Wireless Communications and Mobile Computing (IWCMC), Limassol, Cyprus.","DOI":"10.1109\/IWCMC48107.2020.9148098"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3608","DOI":"10.1109\/TIM.2011.2113124","article-title":"DFT-based Estimation of Damped Oscillation Parameters in Low-Frequency Mechanical Spectroscopy","volume":"60","author":"Duda","year":"2011","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"315","DOI":"10.21595\/jve.2016.16851","article-title":"Ground-penetrating radar time-frequency analysis method based on synchrosqueezing wavelet transformation","volume":"18","author":"Xu","year":"2016","journal-title":"J. Vibroeng."},{"key":"ref_8","first-page":"3467","article-title":"A Low-Cost and Robust Maximum Likelihood Joint Estimator for the Doppler Spread and CFO Parameters Over Flat-Fading Rayleigh Channels","volume":"65","author":"Bellili","year":"2017","journal-title":"IEEE Trans. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2022.3216413","article-title":"Novel Interpolation Method of Multi-DFT-Bins for Frequency Estimation of Signal with Parameter Step Change","volume":"71","author":"Wang","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1868","DOI":"10.1109\/TIM.2014.2381354","article-title":"An Efficient Frequency and Phase Estimation Algorithm with CRB Performance for FMCW Radar Applications","volume":"64","author":"Scherr","year":"2015","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1926","DOI":"10.1109\/TAES.2019.2939611","article-title":"Framework for a Perceptive Mobile Network Using Joint Communication and Radar Sensing","volume":"56","author":"Rahman","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3860","DOI":"10.1109\/JSEN.2020.3028117","article-title":"Fine Doppler Frequency Estimation of Windowed Complex Sinusoidal Signals for Radar Systems","volume":"21","author":"Kim","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1109\/TBME.2004.827930","article-title":"Improved maximum frequency estimation with application to instantaneous mean frequency estimation of surface electromyography","volume":"51","author":"Ostlund","year":"2004","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1109\/TIT.1974.1055282","article-title":"Single tone parameter estimation from discrete-time observations","volume":"20","author":"Rife","year":"1974","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.acha.2021.04.004","article-title":"Fractional Fourier transforms on Lp and applications","volume":"55","author":"Chen","year":"2021","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1109\/78.295186","article-title":"Estimating frequency by interpolation using Fourier coefficients","volume":"42","author":"Quinn","year":"1994","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1109\/78.558515","article-title":"Estimation of frequency, amplitude, and phase from the DFT of a time series","volume":"45","author":"Quinn","year":"1997","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1109\/78.651200","article-title":"Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones","volume":"46","author":"Macleod","year":"1998","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1109\/MSP.2007.361611","article-title":"Fast, Accurate Frequency Estimators [DSP Tips & Tricks]","volume":"24","author":"Jacobsen","year":"2007","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5065","DOI":"10.1109\/TSP.2011.2160257","article-title":"A Noniterative Frequency Estimator with Rational Combination of Three Spectrum Lines","volume":"59","author":"Yang","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1109\/LSP.2013.2273616","article-title":"Analysis and Further Improvement of Fine Resolution Frequency Estimation Method From Three DFT Samples","volume":"20","author":"Candan","year":"2013","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Djukanovi\u0107, S., Popovi\u0107, T., and Mitrovi\u0107, A. (2016, January 22\u201323). Precise sinusoid frequency estimation based on parabolic interpolation. Proceedings of the 2016 24th Telecommunications Forum (TELFOR), Belgrade, Serbia.","DOI":"10.1109\/TELFOR.2016.7818824"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Djukanovi\u0107, S. (2017, January 5\u20137). Sinusoid frequency estimator with parabolic interpolation of periodogram peak. Proceedings of the 2017 40th International Conference on Telecommunications and Signal Processing (TSP), Barcelona, Spain.","DOI":"10.1109\/TSP.2017.8076030"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Fang, L., Duan, D., and Yang, L. (November, January 29). A new DFT-based frequency estimator for single-tone complex sinusoidal signals. Proceedings of the MILCOM 2012\u20142012 IEEE Military Communications Conference, Orlando, FL, USA.","DOI":"10.1109\/MILCOM.2012.6415812"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1109\/TSP.2005.843719","article-title":"Iterative frequency estimation by interpolation on Fourier coefficients","volume":"53","author":"Aboutanios","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1109\/TII.2020.2981542","article-title":"Accurate Frequency Estimation by Using Three-Point Interpolated Discrete Fourier Transform Based on Rectangular Window","volume":"17","author":"Wang","year":"2021","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_28","unstructured":"Dai, X., Tang, T., and Gretsch, R. (1993, January 18\u201320). Quasi-synchronous sampling algorithm and its applications I. Principle and measurement of \u2018average\u2019 values of periodic signal. Proceedings of the 1993 IEEE Instrumentation and Measurement Technology Conference, Irvine, CA, USA."},{"key":"ref_29","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_30","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/TII.2014.2362491","article-title":"Harmonic Estimation Using Symmetrical Interpolation FFT Based on Triangular Self-Convolution Window","volume":"11","author":"Wen","year":"2015","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1109\/LSP.2016.2564102","article-title":"An Accurate Method for Frequency Estimation of a Real Sinusoid","volume":"23","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.sigpro.2017.09.028","article-title":"Frequency estimator of sinusoid based on interpolation of three DFT spectral lines","volume":"144","author":"Fan","year":"2018","journal-title":"Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"44373","DOI":"10.1109\/ACCESS.2020.2977978","article-title":"Accurate Frequency Estimator of Sinusoid Based on Interpolation of FFT and DTFT","volume":"8","author":"Fan","year":"2020","journal-title":"IEEE Access"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2333","DOI":"10.1109\/TCOMM.2018.2886355","article-title":"Fast and Efficient Sinusoidal Frequency Estimation by Using the DFT Coefficients","volume":"67","author":"Serbes","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wei, M., Zhang, A., Qi, L., Li, B., and Sun, J. (2022). An Efficient Frequency Estimator for a Complex Exponential Signal Based on Interpolation of Selectable DTFT Samples. Sensors, 22.","DOI":"10.3390\/s22030861"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.sigpro.2014.05.013","article-title":"A fine-resolution frequency estimator using an arbitrary number of {DFT} coefficients","volume":"105","author":"Orguner","year":"2014","journal-title":"Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/17\/7461\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:40:36Z","timestamp":1760128836000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/17\/7461"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,28]]},"references-count":36,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["s23177461"],"URL":"https:\/\/doi.org\/10.3390\/s23177461","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,28]]}}}