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

Yıl 2022, , 911 - 926, 31.12.2022

Hasan Bayazit , Erdoğan Dilaveroğlu

https://doi.org/10.17482/uumfd.1150894

Öz

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.

Anahtar Kelimeler

Frequency estimation, DFT, Sinc function, Real signals

REEL SİNÜSLERDE AYRIK FOURIER DÖNÜŞÜMÜNÜN ÜÇ ÖRNEĞİNE DAYALI FREKANS KESTİRİMİ

Öz

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.

Anahtar Kelimeler

Frekans kestirimi, Ayrık Fourier dönüşümü, Sinc fonksiyonu, Reel sinyaller

Kaynakça

• 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