Research Article
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Frequency Estimation Based on Three Samples of Discrete Fourier Transform in Real Sinusoids

Year 2022, Volume: 27 Issue: 3, 911 - 926, 31.12.2022
https://doi.org/10.17482/uumfd.1150894

Abstract

In this study, the behavior of parabolic, Jacobsen, bias-corrected Jacobsen, and Quinn estimators, which are used in frequency estimation and based on three samples of discrete Fourier transform, are examined on real signals comparatively. As an alternative to these estimators, a sinc function-based frequency estimator is proposed, and the root means square errors (RMSE) of the estimator are compared by performing computer simulations. It has been observed that the proposed sinc-based estimator gives lower RMS errors in a wide part of the frequency range compared to other estimators.

References

  • 1. Bergland, G.D. (1969) A guided tour of the fast Fourier Transform, IEEE Spectrum. doi: 10.1109/MSPEC.1969.5213896
  • 2. Borkowski, J., Kania, D., Mroczka, J. (2015) Interpolated DFT-Based Fast and Accurate Frequency Estimation for the Control of Power, IEEE Transactions on Industrial Electronics vol. 61,No 12. doi: 10.1109/TIE.2014.2316225
  • 3. Candan, Ç. (2011) A Method For Fine Resolution Frequency Estimation From Three DFT Samples, IEEE Signal Processing Letters vol. 18, No.6. doi: 10.1109/LSP.2011.2136378
  • 4. Candan, Ç. (2013) Analysis and Further Improvement of Fine Resolution Frequency Estimation Method From Three DFT Samples, IEEE Signal Processing Letters vol. 20. doi: 10.1109/LSP.2013.2273616
  • 5. Fu, L.,Li, H. (2006) Wavelet-based Approach for Frequency Estimation in Complex Noises, ICSP 2006 Proceedings. doi: 10.1109/ICOSP.2006.344500
  • 6. Grandke, T. (1983) Interpolation algorithms for discrete Fourier Transforms of weighted signals, IEEE Transactions on Instrumentation and Measurement ol.32. doi: 10.1109/TIM. 1983.4315077
  • 7. https://bigsoundbank.com/detail-0218-heart-beat.html, Erişim Tarihi: 6.11.2022, Konu: Kalp atış sinyali.
  • 8. Hussain, A., Ivanovic, M. (2015) Electronics, Communications and Networks IV, CRC Press, volume 1.
  • 9. Jacobsen, E., Kootsookos, P. (2007), Fast, Accurate Frequency Estimator, IEEE Signal Processing Magazine. doi: 10.1109/MSP.2007.361611
  • 10. Nielsen, J. K., Jensen, T.L., Jensen J.R., Christensen, M.G., Jensen, S.H. Liu, S.; Wang, L. (2015) A Fast Algorithm for Maximum Likelihood-Based Fundamental Frequency Estimation, 23rd European Signal Processing Conference. doi:10.1109/ EUSIPCO. 2015. 7362451
  • 11. Prabhu, K.M.M. (2014) Window Functions and Their Applications, CRC Press.
  • 12. Quinn, B.G. (1994) Estimating Frequency by Interpolation Using Fourier Coefficients, IEEE Trans. Signal Processing vol. 42. doi: 10.1109/78.295186
  • 13. Rapuano, S., Harris F. (2007) An Introduction to FFT and Time Domain Windows, IEEE Instumentation & Measurement Magazine. doi: 10.1109/MIM.2007.4428580
  • 14. Richard G. L. (2011) Understanding Digital Signal Processing, Prentice-Hall Third Edition.
  • 15. Rife, D.C.; Boorstyn, R.R (1974) Fast, Single Tone Parameter Estimation for Discrete_Time Observations. IEEE Transactions on Information Theory, IT-20, 123-125.
  • 16. Voglewede, P. (2004) Parabola approximation for peak determination, Global DSP Magazine vol 3,13-17.
  • 17. Zhang, J.; Liu, S.; Tang, L.; Mingotti, A.; Peretto, L.; Wen, H. (2020) Analysis of White Noise on Power Frequency Estimation by DFT-Based Frequency Shifting and Filtering, IEEE Transactions on Instrumentation and Measurement vol 69, 4125-4132. doi:10.1109/TIM. 2019.2941290

REEL SİNÜSLERDE AYRIK FOURIER DÖNÜŞÜMÜNÜN ÜÇ ÖRNEĞİNE DAYALI FREKANS KESTİRİMİ

Year 2022, Volume: 27 Issue: 3, 911 - 926, 31.12.2022
https://doi.org/10.17482/uumfd.1150894

Abstract

Bu çalışmada, frekans kestiriminde kullanılan ve ayrık Fourier dönüşümün üç örneğine dayanan parabolik, Jacobsen, yanlılığı düzeltilmiş Jacobsen ve Quinn kestiricilerinin reel sinyaller üzerindeki davranışları karşılaştırmalı olarak incelenmiştir. Bu kestiricilere alternatif olarak bir sinc fonksiyonu tabanlı frekans kestiricisi önerilmiş ve kestiricinin karesel ortalamalarının karekökü hataları (RMSE) bilgisayar benzetimleri yapılarak karşılaştırılmıştır. Önerilen sinc tabanlı kestirici, frekans aralığının geniş bir kısmında diğer kestiricilere göre düşük RMSE değerleri verdiği gözlenmiştir.

References

  • 1. Bergland, G.D. (1969) A guided tour of the fast Fourier Transform, IEEE Spectrum. doi: 10.1109/MSPEC.1969.5213896
  • 2. Borkowski, J., Kania, D., Mroczka, J. (2015) Interpolated DFT-Based Fast and Accurate Frequency Estimation for the Control of Power, IEEE Transactions on Industrial Electronics vol. 61,No 12. doi: 10.1109/TIE.2014.2316225
  • 3. Candan, Ç. (2011) A Method For Fine Resolution Frequency Estimation From Three DFT Samples, IEEE Signal Processing Letters vol. 18, No.6. doi: 10.1109/LSP.2011.2136378
  • 4. Candan, Ç. (2013) Analysis and Further Improvement of Fine Resolution Frequency Estimation Method From Three DFT Samples, IEEE Signal Processing Letters vol. 20. doi: 10.1109/LSP.2013.2273616
  • 5. Fu, L.,Li, H. (2006) Wavelet-based Approach for Frequency Estimation in Complex Noises, ICSP 2006 Proceedings. doi: 10.1109/ICOSP.2006.344500
  • 6. Grandke, T. (1983) Interpolation algorithms for discrete Fourier Transforms of weighted signals, IEEE Transactions on Instrumentation and Measurement ol.32. doi: 10.1109/TIM. 1983.4315077
  • 7. https://bigsoundbank.com/detail-0218-heart-beat.html, Erişim Tarihi: 6.11.2022, Konu: Kalp atış sinyali.
  • 8. Hussain, A., Ivanovic, M. (2015) Electronics, Communications and Networks IV, CRC Press, volume 1.
  • 9. Jacobsen, E., Kootsookos, P. (2007), Fast, Accurate Frequency Estimator, IEEE Signal Processing Magazine. doi: 10.1109/MSP.2007.361611
  • 10. Nielsen, J. K., Jensen, T.L., Jensen J.R., Christensen, M.G., Jensen, S.H. Liu, S.; Wang, L. (2015) A Fast Algorithm for Maximum Likelihood-Based Fundamental Frequency Estimation, 23rd European Signal Processing Conference. doi:10.1109/ EUSIPCO. 2015. 7362451
  • 11. Prabhu, K.M.M. (2014) Window Functions and Their Applications, CRC Press.
  • 12. Quinn, B.G. (1994) Estimating Frequency by Interpolation Using Fourier Coefficients, IEEE Trans. Signal Processing vol. 42. doi: 10.1109/78.295186
  • 13. Rapuano, S., Harris F. (2007) An Introduction to FFT and Time Domain Windows, IEEE Instumentation & Measurement Magazine. doi: 10.1109/MIM.2007.4428580
  • 14. Richard G. L. (2011) Understanding Digital Signal Processing, Prentice-Hall Third Edition.
  • 15. Rife, D.C.; Boorstyn, R.R (1974) Fast, Single Tone Parameter Estimation for Discrete_Time Observations. IEEE Transactions on Information Theory, IT-20, 123-125.
  • 16. Voglewede, P. (2004) Parabola approximation for peak determination, Global DSP Magazine vol 3,13-17.
  • 17. Zhang, J.; Liu, S.; Tang, L.; Mingotti, A.; Peretto, L.; Wen, H. (2020) Analysis of White Noise on Power Frequency Estimation by DFT-Based Frequency Shifting and Filtering, IEEE Transactions on Instrumentation and Measurement vol 69, 4125-4132. doi:10.1109/TIM. 2019.2941290
There are 17 citations in total.

Details

Primary Language Turkish
Subjects Communication and Media Studies, Electrical Engineering
Journal Section Research Articles
Authors

Hasan Bayazit 0000-0002-8099-3190

Erdoğan Dilaveroğlu 0000-0002-8432-623X

Early Pub Date December 9, 2022
Publication Date December 31, 2022
Submission Date July 29, 2022
Acceptance Date November 18, 2022
Published in Issue Year 2022 Volume: 27 Issue: 3

Cite

APA Bayazit, H., & Dilaveroğlu, E. (2022). REEL SİNÜSLERDE AYRIK FOURIER DÖNÜŞÜMÜNÜN ÜÇ ÖRNEĞİNE DAYALI FREKANS KESTİRİMİ. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, 27(3), 911-926. https://doi.org/10.17482/uumfd.1150894
AMA Bayazit H, Dilaveroğlu E. REEL SİNÜSLERDE AYRIK FOURIER DÖNÜŞÜMÜNÜN ÜÇ ÖRNEĞİNE DAYALI FREKANS KESTİRİMİ. UUJFE. December 2022;27(3):911-926. doi:10.17482/uumfd.1150894
Chicago Bayazit, Hasan, and Erdoğan Dilaveroğlu. “REEL SİNÜSLERDE AYRIK FOURIER DÖNÜŞÜMÜNÜN ÜÇ ÖRNEĞİNE DAYALI FREKANS KESTİRİMİ”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 27, no. 3 (December 2022): 911-26. https://doi.org/10.17482/uumfd.1150894.
EndNote Bayazit H, Dilaveroğlu E (December 1, 2022) REEL SİNÜSLERDE AYRIK FOURIER DÖNÜŞÜMÜNÜN ÜÇ ÖRNEĞİNE DAYALI FREKANS KESTİRİMİ. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 27 3 911–926.
IEEE H. Bayazit and E. Dilaveroğlu, “REEL SİNÜSLERDE AYRIK FOURIER DÖNÜŞÜMÜNÜN ÜÇ ÖRNEĞİNE DAYALI FREKANS KESTİRİMİ”, UUJFE, vol. 27, no. 3, pp. 911–926, 2022, doi: 10.17482/uumfd.1150894.
ISNAD Bayazit, Hasan - Dilaveroğlu, Erdoğan. “REEL SİNÜSLERDE AYRIK FOURIER DÖNÜŞÜMÜNÜN ÜÇ ÖRNEĞİNE DAYALI FREKANS KESTİRİMİ”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 27/3 (December 2022), 911-926. https://doi.org/10.17482/uumfd.1150894.
JAMA Bayazit H, Dilaveroğlu E. REEL SİNÜSLERDE AYRIK FOURIER DÖNÜŞÜMÜNÜN ÜÇ ÖRNEĞİNE DAYALI FREKANS KESTİRİMİ. UUJFE. 2022;27:911–926.
MLA Bayazit, Hasan and Erdoğan Dilaveroğlu. “REEL SİNÜSLERDE AYRIK FOURIER DÖNÜŞÜMÜNÜN ÜÇ ÖRNEĞİNE DAYALI FREKANS KESTİRİMİ”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, vol. 27, no. 3, 2022, pp. 911-26, doi:10.17482/uumfd.1150894.
Vancouver Bayazit H, Dilaveroğlu E. REEL SİNÜSLERDE AYRIK FOURIER DÖNÜŞÜMÜNÜN ÜÇ ÖRNEĞİNE DAYALI FREKANS KESTİRİMİ. UUJFE. 2022;27(3):911-26.

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