Fig. 1. Direction of CW signals and geometry of VLA (Vertical Line Array).
Fig. 2. Frequency-wavenumber spectrum from 3-directions CW signal.
Fig. 3. LFM signal for free space simulation.
Fig. 4. Frequency-wavenumber spectrum from 1-direction LFM signal.
Fig. 7. Applying Radon transform to frequency wavenumber spectrum.
Fig. 8. Frequency-wavenumber spectrum from 3-directions LFM signal.
Fig. 9. The result of the Radon transform when the Radon domain is set to 2 kHz
Fig. 10. Shrimp signal in SAVEX15.
Fig. 11. Spectrogram of shrimp signal (ch #16, direct path).
Fig. 12. The frequency-wavenumber spectrum of the shrimp signal.
Fig. 13. The result of the Radon transform when the Radon domain is set to 20 kHz.
Fig. 14. The result of CBF (upper) and FDBF (lower) in frequency domain.
Fig. 15. Comparison among CBF, FDBF and the proposed algorithm.
Fig. 16. Comparison of results of frequency-difference beamforming according to difference frequency components.
Fig. 5. Beam pattern in 2 kHz.
Fig. 6. Projection data.[15]
References
- M. J. Hinch, "Frequency-wavenumber array processing," J. Acoust. Soc. Am. 69, 732-737 (1981). https://doi.org/10.1121/1.385572
- S. H. Abadi, H. C. Hong, and D. R. Dawling, "Broadband sparse array blind-deconvolution using frequencydifference beamforming," J. Acoust. Soc. Am. 132, 3018-3029 (2012). https://doi.org/10.1121/1.4756920
- G. F. Edelmann and C. F. Gaumond, "Beamforming using compressive sensing," J. Acoust. Soc. Am. 130, EL232-EL237 (2011). https://doi.org/10.1121/1.3632046
- J. Capon, "High resolution frequency wavenumber spectrum analysis," Proc. IEEE, 57, 1408-1418 (1969). https://doi.org/10.1109/PROC.1969.7278
- J. Wang, H. Cetinkaya, and A. Yarovoy, "NUFFT based frequency-wavenumber domain focusing under MIMO array configurations," Radar Conference, 2014 IEEE. IEEE, 1-5 (2014).
- K. Liu, F. Liu, S. Wei, and G. Wang, "Target depth extraction based on the character of sound field vertical wavenumber spectrum," Ocean Acoustics (COA), 2016 IEEE/OES China. IEEE (2016).
- C. J. Geoga, C. L. Haley, A. R. Siegel, and M. Anitescu, "Frequency-wavenumber spectral analysis of spatio-temporal flows," J. Fluid Mechanics, 848, 545-559 (2018). https://doi.org/10.1017/jfm.2018.366
- J. Dmochowski, J. Benesty, and S. Affes, "On spatial aliasing in microphone arrays," IEEE Transactions on Signal Processing, 57, 1383-1395 (2009). https://doi.org/10.1109/TSP.2008.2010596
- F. Pinto, M. Kolundzija, and M. Vetterli, "Digital acoustics: processing wave fields in space and time using DSP tools," APSIPA Transactions on Signal and Information Processing, 3 (2014).
- S. R. Deans, The Radon Transform and Some of its Applications (Courier Corporation, New York, 2007), pp. 55-60.
- G. Beylkin, "Discrete radon transform," Acoustics, Speech and Signal Process., IEEE Trans. 35, 162-172 (2003). https://doi.org/10.1109/TASSP.1987.1165108
- D. Y. Park and H. Yoo, "CT Reconstruction using Discrete Cosine Transform with non-zero DC Components," Trans. Korean. Inst. Elect. Eng. 63, 1001-1007 (2014). https://doi.org/10.5370/KIEE.2014.63.7.1001
- A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE press, New York, 1988), pp. 28-46.
- E. Masry, "The estimation of the frequency‐wavenumber spectrum using random acoustic arrays-Part II. A class of consistent estimators," J. Acoust. Soc. Am. 76, 1123-1131 (1984). https://doi.org/10.1121/1.391404
- D. Rouseff and L. M. Zurk, "Striation-based beamforming for estimating the waveguide invariant with passive sonar," J. Acoust. Soc. Am. 130, EL76-EL81 (2011). https://doi.org/10.1121/1.3606571
- A. S. Douglass, H. C. Song, and D. R. Dowling, "Performance comparisons of frequency-difference and conventional beamforming," J. Acoust. Soc. Am. 142, 1663-1673 (2011). https://doi.org/10.1121/1.5003787