Abstract
In order to alleviate the effect of additive noise and to reduce the computational burden, we proposed a new computationally efficient cross-correlation based two-dimensional frequency estimation method for multiple real valued sinusoidal signals. Here the frequencies of both the dimensions are estimated independently with a one-dimensional (1-D) subspace-based estimation technique without eigendecomposition, where the null spaces are obtained through a linear operation of the matrices formed from the cross-correlation matrix between the received data. The estimated frequencies in both the dimensions are automatically paired. Simulation results show that the proposed method offers competitive performance when compared to existing approaches at a lower computational complexity. It has shown that proposed method perform well at low signal-to-noise ratio (SNR) and with a small number of snapshots.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Francos JM, Friedlander B (1998) Parameter estimation of two-dimensional moving average random fields. IEEE Trans Signal Process 46:2157–2165
Wang H, Williams K (1996) Vibrational modes of cylinders of finite length. J Sound Vib 191(5):955–971
Verma S, Singal R, Williams K (1987) Vibration behavior of stators of electrical machines, part I: theoretical study. J Sound Vib 115(1):1–12
Singal R, Williams K, Verma S (1987) Vibration behavior of stators of electrical machines, part II: experimental study. J Sound Vib 115(1):13–23
Zhang XM (2001) Vibration analysis of cross-ply laminated composite cylindrical shells using the wave propagation approach. Appl Acoust 62:1221–1228
So J, Leissa A (1998) Three-dimensional vibrations of thick circular and annular plates. J Sound Vib 209(1):15–41
Skatter S (1996) TV holography as a possible tool for measuring transversevibration of logs: a pilot study. Wood Fiber Sci 28(3):278–285
Axmon J, Hansson M (1999) Estimation of circumferential mode parameters of living trees. In: Proceedings of the IASTED international conference on signal image process (SIP’99), pp 188–192
Axmon J (2000) On detection of decay in growing norway spruce via natural frequencies. Licentiate of Engineering Thesis Lund University. Lund, Sweden, Oct 2000
Axmon J, Hansson M, Sörnmo L (2002) Modal analysis of living spruce using a combined Prony and DFT multichannel method for detection of internal decay. Mech Syst Signal Process 16(4):561–584
Hua Y (1992) Estimating two-dimensional frequencies by matrix enhancement and matrix pencil. IEEE Trans Signal Process 40(9):2267–2280
Haardt M, Roemer F, DelGaldo G (2008) Higher-order SVD-based subspace estimation to improve the parameter estimation accuracy in multidimensional harmonic retrieval problems. IEEE Trans Signal Process 56(7):3198–3213
Mahata K (2005) Subspace fitting approaches for frequency estimation using real-valued data. IEEE Trans Signal process 53(8):3099–3110
Palanisamy P, Sambit PK (2011) Estimation of real-valued sinusoidal signal frequencies based on ESPRIT and propagator method. In: Proceedings of the IEEE-international conference on recent trends in information technology, pp 69–73 June 2011
Stoica P, Eriksson A (1995) MUSIC estimation of real-valued sine-wave frequencies. Signal process 42(2):139–146
Priestley MB (1981) Spectral analysis and time series. Academic, New York
Walker M (1971) On the estimation of a harmonic component in a time series with stationary independent residuals. Biometrika 58:21–36
Rao CR, Zhao L, Zhou B (1994) Maximum likelihood estimation of 2-D superimposed exponential signals. IEEE Trans Signal Process 42:1795–1802
Kundu D, Mitra A (1996) Asymptotic properties of the least squares estimates of 2-D exponential signals. Multidim Syst Signal Process 7:135–150
Lang SW, McClellan JH (1982) The extension of Pisarenko’s method to multiple dimensions. In: Proceedings of the international conference on acoustics, speech, and signal processing, pp 125–128
Kumaresan R, Tufts DW (1981) A two-dimensional technique for frequency wave number estimation. Proc IEEE 69:1515–1517
Axmon J, Hansson M, Sörnmo L (2005) Partial forward–backward averaging for enhanced frequency estimation of real X-texture modes. IEEE Trans Signal Process 53(7):2550–2562
So HC, Chan FKW, Chan CF (2010) Utilizing principal singular vectors for two-dimensional single frequency estimation. In: Proceedings of the IEEE international conference on acoustics, speech, signal process, pp 3882–3886, March 2010
Xin J, Sano A (2004) Computationally efficient subspace-based method for direction-of-arrival estimation without eigen decomposition. IEEE Trans Signal process 52(4):876–893
Sambit PK, Palanisamy P (2012) A propagator method like algorithm for estimation of multiple real-valued sinusoidal signal frequencies. Int J Electron Electr Eng 6:254–258
Marcos S, Marsal A, Benidir M (1995) The propagator method for source bearing estimation. Signal Process 42(2):121–138
Golub GH, Van Loan CF (1980) An analysis of the total least squares problem. SIAM J Numer Anal 17:883–893
Rouquette S, Najim M (2001) Estimation of frequencies and damping factors by two-dimensional ESPRIT type methods. IEEE Trans Signal Process 49(1):237–245
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer India
About this paper
Cite this paper
Sambit, P.K., Palanisamy, P. (2013). An Efficient Two Dimensional Multiple Real-Valued Sinusoidal Signal Frequency Estimation Algorithm. In: S, M., Kumar, S. (eds) Proceedings of the Fourth International Conference on Signal and Image Processing 2012 (ICSIP 2012). Lecture Notes in Electrical Engineering, vol 221. Springer, India. https://doi.org/10.1007/978-81-322-0997-3_9
Download citation
DOI: https://doi.org/10.1007/978-81-322-0997-3_9
Published:
Publisher Name: Springer, India
Print ISBN: 978-81-322-0996-6
Online ISBN: 978-81-322-0997-3
eBook Packages: EngineeringEngineering (R0)