A Comparative Study of FFT Based Frequency Estimation Using Different Interpolation Techniques

Section: Research Paper
Published
Sep 1, 2023
Pages
86-93

Abstract

Fast Fourier Transform (FFT) is a commonly used method in electronic support systems for frequency parameter estimation. If the frequency of the radar signal is not an exact multiple of the frequency resolution, the frequency of this signal will usually appear in an inter-line position when FFT is applied. To improve the accuracy of the estimated frequency, interpolation techniques are used to find the peak between two spectral lines. In this study, the frequency of the radar signal is estimated by employing three different interpolation techniques (Ding, Voglewede and Hanning window based interpolation) to the output obtained by applying N-point FFT to the intermediate frequency (IF) signal. In addition, unlike the literature, the behavior of signals contaminated with Laplace noise as well as Gaussian noise were analyzed with these three techniques and their performances were compared. From the analysis results, Ding and Voglewede techniques reduced error rate at all frequency. However, the Hanning window-based interpolation method improved the frequency accuracy values at 500MHz and 750MHz, but it increased the error at 250MHz and 1000MHz frequencies. The error rates of the estimated frequencies can be sorted from the lowest to the highest as follows: Ding, Voglewede and Hanning window based interpolation.

References

  1. A. A. Minda, C.-I. Barbinita, and G. R. Gillich, A Review of Interpolation Methods Used for Frequency Estimation, Rom. J. Acoust. Vib., vol. 17, no. 1, pp. 2126, 2020.
  2. A. A. Minda, D. Lupu, and G.-R. Gillich, Improvement of Jains algorithm for frequency estimation, Stud. Univ. Babes-Bolyai Eng., vol. 65, no. 1, 2020.
  3. B. G. Quinn, Estimating frequency by interpolation using Fourier coefficients, IEEE Trans. Signal Process., vol. 42, no. 5, pp. 12641268, 1994.
  4. B. K. A. Abdulhamed, Digital Instantaneous Frequency Measurement Receiver for Fine Frequency and High Sensitivity, 2019.
  5. B. Yang, K. Dai, C. Yang, H. Luo, K. He, and Z. Dai, Improvement of recursive DFT for APF with higher switching frequency to suppress wideband harmonics, IEEE Access, vol. 9, pp. 144300144312, 2021.
  6. . Candan, A method for fine resolution frequency estimation from three DFT samples, IEEE Signal Process. Lett., vol. 18, no. 6, pp. 351354, 2011.
  7. . Candan, Fine resolution frequency estimation from three DFT samples: Case of windowed data, Signal Processing, vol. 114, pp. 245250, 2015.
  8. C. Peeters et al., Review and comparison of tacholess instantaneous speed estimation methods on experimental vibration data, Mech. Syst. Signal Process., vol. 129, pp. 407436, 2019, doi: 10.1016/j.ymssp.2019.02.031.
  9. E. Jacobsen and P. Kootsookos, Fast, accurate frequency estimators [DSP Tips & Tricks], IEEE Signal Process. Mag., vol. 24, no. 3, pp. 123125, 2007.
  10. G. Cabada and K. mer, Analysis of Pronys and Pisarenko Frequency Estimation Methods at Different Bandwidths, Different Noise And Variances, 30th Signal Processing and Communications Applications Conference (SIU), 2022.
  11. . E. Ortatatl, A. Orduylmaz, M. Serin, . zdil, A. Yldrm, and A. C. Grbz, Real-time frequency parameter extraction for electronic support systems, in 2016 24th Signal Processing and Communication Application Conference (SIU), 2016, pp. 105108.
  12. J. B. Tsui, Digital techniques for wideband receivers, vol. 2. SciTech Publishing, 2004.
  13. J. Borkowski, D. Kania, and J. Mroczka, Comparison of sine-wave frequency estimation methods in respect of speed and accuracy for a few observed cycles distorted by noise and harmonics, Metrol. Meas. Syst., vol. 25, no. 2, 2018.
  14. K. Duda, DFT interpolation algorithm for KaiserBessel and DolphChebyshev windows, IEEE Trans. Instrum. Meas., vol. 60, no. 3, pp. 784790, 2011.
  15. K. H. Sayidmarie and S. E. Abdul-Fatah, The Effet of the Height and Speed of the Airplane Carrying the Focused Synthetic Aperture Radar on the Azimuth Resolution, Al-Rafidain Eng. J., vol. 13, no. 4, 2005.
  16. K. Ibrahim Ali Al-Sharabi and D. Fiz, Design of wideband radio direction finder based on amplitude comparison, Al-Rafidain Eng. J., vol. 19, no. 5, pp. 7786, 2011.
  17. K. Ibrahim Ali Al-Sharabi, A SimpleMethod to Derive the Bistatic Tracking Radar System Formulas, Al-Rafidain Eng. J., vol. 20, no. 2, pp. 140149, 2012.
  18. L. Fang, D. Duan, and L. Yang, A new DFT-based frequency estimator for single-tone complex sinusoidal signals, in MILCOM 2012-2012 IEEE Military Communications Conference, 2012, pp. 16.
  19. M. C. Arva, N. Bizon, and A. Micu, Proposal of an accurate and low complexity method for frequency estimation using DFT interpolation, in 2017 40th International Conference on Telecommunications and Signal Processing (TSP), 2017, pp. 474479.
  20. M. Gasior and J. L. Gonzalez, Improving FFT frequency measurement resolution by parabolic and Gaussian spectrum interpolation, in AIP Conference Proceedings, 2004, vol. 732, no. 1, pp. 276285.
  21. M. Ko, Baz Ayrk Fourier Dnmne Dayal Frekans Kestiricilerin Karlatrmal Performans Analizi. Bursa Uludag University (Turkey), 2021.
  22. . Karal, Maximum likelihood optimal and robust support vector regression with lncosh loss function, Neural Networks, 2017.
  23. R. K. Niranjan, C. B. R. Rao, and A. K. Singh, Performance Comparison of FFT based Frequency Estimation using different Interpolation Techniques for ELINT Systems, in 2021 International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT), 2021, pp. 14.
  24. V. Iglesias, J. Grajal, O. Yeste-Ojeda, M. Garrido, M. A. Snchez, and M. Lpez-Vallejo, Real-time radar pulse parameter extractor, in 2014 IEEE Radar Conference, 2014, pp. 371375.
  25. Y. Liu, C. Wang, J. Sun, S. Du, and Q. Hong, One-step calculation circuit of fft and its application, IEEE Trans. Circuits Syst. I Regul. Pap., vol. 69, no. 7, pp. 27812793, 2022.
  26. Yazc, Z.B., Hasimoglu S,. Comparison of a random model of Hand-Foot-Mouth Disease model with Gaussian and Laplacian parameters, Gmhane niversitesi Fen Bilim. Derg., vol. 12, no. 1, pp. 925, 2019.
  27. Z. Lai et al., Application of FFT interpolation correction algorithm based on window function in power harmonic analysis, in IOP Conference Series: Earth and Environmental Science, 2019, vol. 252, no. 3, p. 32184.
Download this PDF file

Statistics

How to Cite

[1]
G. Cabadağ and Ömer Karal, “A Comparative Study of FFT Based Frequency Estimation Using Different Interpolation Techniques”, AREJ, vol. 28, no. 2, pp. 86–93, Sep. 2023.