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Chirp Signal Model

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Statistical Signal Processing

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Abstract

Chirp signals have played an important role in the statistical signal processing literature. An extensive amount of work has been done in analyzing different one dimensional chirp, two dimensional chirp and some related signal processing models. These models have been used in analyzing different real-life signals or images quite efficiently. It is observed that several sophisticated statistical and computational techniques are needed to analyze these models and in developing estimation procedures. In this chapter a comprehensive review of different models have been presented, and several open problems are discussed for future research.

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References

  1. Abatzoglou, T. (1986). Fast maximum likelihood joint estimation of frequency and frequency rate. IEEE Transactions on Aerospace and Electronic Systems, 22, 708–715.

    Google Scholar 

  2. Amar, A., Leshem, A., & van der Veen, A. J. (2010). A low complexity blind estimator of narrow-band polynomial phase signals. IEEE Transactions on Signal Processing, 58, 4674–4683.

    MathSciNet  MATH  Google Scholar 

  3. Bai, Z. D., Rao, C. R., Chow, M., & Kundu, D. (2003). An efficient algorithm for estimating the parameters of superimposed exponential signals. Journal of Statistical Planning and Inference, 110, 23–34.

    MathSciNet  MATH  Google Scholar 

  4. Benson, O., Ghogho, M., & Swami, A. (1999). Parameter estimation for random amplitude chirp signals. IEEE Transactions on Signal Processing, 47, 3208–3219.

    Google Scholar 

  5. Besson, O., Giannakis, G. B., & Gini, F. (1999). Improved estimation of hyperbolic frequency modulated chirp signals. IEEE Transactions on Signal Processing., 47, 1384–1388.

    Google Scholar 

  6. Cao, F.,Wang, S., & Wang, F. (2006). Cross-spectral method based on 2-D cross polynomial transform for 2-D chirp signal parameter estimation. In ICSP2006 Proceedings. https://doi.org/10.1109/ICOSP.2006.344475.

  7. Dhar, S. S., Kundu, D., & Das, U. (2019). On testing parameters of chirp signal model. IEEE Transactions on Signal Processing, 67, 4291–4301.

    MathSciNet  MATH  Google Scholar 

  8. Djurić, P. M., & Kay, S. M. (1990). Parameter estimation of chirp signals. IEEE Transactions on Acoustics, Speech and Signal Processing, 38, 2118–2126.

    Google Scholar 

  9. Djukanović, S., & Djurović, I. (2012). Aliasing detection and resolving in the estimation of polynomial-phase signal parameters. Signal Processing, 92, 235–239.

    Google Scholar 

  10. Djurović, I., Simeunović, M., & Wang, P. (2017). Cubic phase function: A simple solution for polynomial phase signal analysis. Signal Processing, 135, 48–66.

    Google Scholar 

  11. Djurović, I., & Stanković, L. J. (2014). Quasi maximum likelihood estimators of polynomial phase signals. IET Signal Processing, 13, 347–359.

    Google Scholar 

  12. Djurović, I., Wang, P., & Ioana, C. (2010). Parameter estimation of 2-D cubic phase signal function using genetic algorithm. Signal Processing, 90, 2698–2707.

    MATH  Google Scholar 

  13. Farquharson, M., O’Shea, P., & Ledwich, G. (2005). A computationally efficient technique for estimating the parameters phase signals from noisy observations. IEEE Transactions on Signal Processing, 53, 3337–3342.

    MathSciNet  MATH  Google Scholar 

  14. Fourier, D., Auger, F., Czarnecki, K., & Meignen, S. (2017). Chirp rate and instantaneous frequency estimation: application to recursive vertical synchrosqueezing. IEEE Signal Processing Letters, 24, 1724–1728.

    Google Scholar 

  15. Francos, J. M., & Friedlander, B. (1998). Two-dimensional polynomial phase signals: Parameter estimation and bounds. Multidimensional Systems and Signal Processing, 9, 173–205.

    MathSciNet  MATH  Google Scholar 

  16. Francos, J. M., & Friedlander, B. (1999). Parameter estimation of 2-D random amplitude polynomial phase signals. IEEE Transactions on Signal Processing, 47, 1795–1810.

    MathSciNet  MATH  Google Scholar 

  17. Friedlander, B., & Francos, J. M. (1996). An estimation algorithm for 2-D polynomial phase signals. IEEE Transactions on Image Processing, 5, 1084–1087.

    Google Scholar 

  18. Gabor, D. (1946). Theory of communication. Part 1: The analysis of information. Journal of the Institution of Electrical Engineers - Part III: Radio and Communication Engineering, 93, 429–441.

    Google Scholar 

  19. Gini, F., Montanari, M., & Verrazzani, L. (2000). Estimation of chirp signals in compound Gaussian clutter: A cyclostationary approach. IEEE Transactions on Acoustics, Speech and Signal Processing, 48, 1029–1039.

    MATH  Google Scholar 

  20. Grover, R., Kundu, D., & Mitra, A. (2018). On approximate least squares estimators of parameters of one-dimensional chirp signal. Statistics, 52, 1060–1085.

    MathSciNet  MATH  Google Scholar 

  21. Grover, R., Kundu, D., & Mitra, A. (2018). Asymptotic of approximate least squares estimators of parameters of two-dimensional chirp signal. Journal of Multivariate Analysis, 168, 211–220.

    MathSciNet  MATH  Google Scholar 

  22. Gu, T., Liai, G., Li, Y., Guo, Y., & Huang, Y. (2020). Parameter estimation of multicomponent LFM signals based on GAPCK. Digital Signal Processing, 100. Article ID. 102683.

    Google Scholar 

  23. Guo, J., Zou, H., Yang, X., & Liu, G. (2011). Parameter estimation of multicomponent chirp signals via sparse representation. IEEE Transactions on Aerospace and Electronic Systems, 47, 2261–2268.

    Google Scholar 

  24. Hedley, M., & Rosenfeld, D. (1992). A new two-dimensional phase unwrapping algorithm for MRI images. Magnetic Resonance in Medicine, 24, 177–181.

    Google Scholar 

  25. Ikram, M. Z., Abed-Meraim, K., & Hua, Y. (1998). Estimating the parameters of chirp signals: An iterative aproach. IEEE Transactions on Signal Processing, 46, 3436–3441.

    Google Scholar 

  26. Ikram, M. Z., & Zhou, G. T. (2001). Estimation of multicomponent phase signals of mixed orders. Signal Processing, 81, 2293–2308.

    MATH  Google Scholar 

  27. Jennrich, R. I. (1969). Asymptotic properties of the nonlinear least squares estimators. Annals of Mathematical Statistics, 40, 633–643.

    MathSciNet  MATH  Google Scholar 

  28. Kennedy, W. J, Jr., & Gentle, J. E. (1980). Statistical Computing. New York: Marcel Dekker Inc.

    MATH  Google Scholar 

  29. Kim, G., Lee, J., Kim, Y., & Oh, H.-S. (2015). Sparse Bayesian representation in time-frequency domain. Journal of Statistical Planning and Inference, 166, 126–137.

    MathSciNet  MATH  Google Scholar 

  30. Kundu, D., & Nandi, S. (2003). Determination of discrete spectrum in a random field. Statistica Neerlandica, 57, 258–283.

    MathSciNet  MATH  Google Scholar 

  31. Kundu, D., & Nandi, S. (2008). Parameter estimation of chirp signals in presence of stationary Christensen, noise. Statistica Sinica, 18, 187–201.

    MathSciNet  MATH  Google Scholar 

  32. Lahiri, A. (2011). Estimators of parameters of chirp signals and their properties. Ph.D. Dissertation, Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India.

    Google Scholar 

  33. Lahiri, A., & Kundu, D. (2017). On parameter estimation of two-dimensional polynomial phase signal model. Statistica Sinica, 27, 1779–1792.

    MathSciNet  MATH  Google Scholar 

  34. Lahiri, A., Kundu, D., & Mitra, A. (2012). Efficient algorithm for estimating the parameters of chirp signal. Journal of Multivariate Analysis, 108, 15–27.

    MathSciNet  MATH  Google Scholar 

  35. Lahiri, A., Kundu, D., & Mitra, A. (2013). Efficient algorithm for estimating the parameters of two dimensional chirp signal. Sankhya Series B, 75, 65–89.

    MathSciNet  MATH  Google Scholar 

  36. Lahiri, A., Kundu, D., & Mitra, A. (2014). On least absolute deviation estimator of one dimensional chirp model. Statistics, 48, 405–420.

    MathSciNet  MATH  Google Scholar 

  37. Lahiri, A., Kundu, D., & Mitra, A. (2015). Estimating the parameters of multiple chirp signals. Journal of Multivariate Analysis, 139, 189–205.

    MathSciNet  MATH  Google Scholar 

  38. Lin, C-C., & Djurić, P. M. (2000). Estimation of chirp signals by MCMC. ICASSP-1998, 1, 265–268.

    Google Scholar 

  39. Liu, X., & Yu, H. (2013). Time-domain joint parameter estimation of chirp signal based on SVR. Mathematical Problems in Engineering. Article ID: 952743.

    Google Scholar 

  40. Lu, Y., Demirli, R., Cardoso, G., & Saniie, J. (2006). A successive parameter estimation algorithm for chirplet signal decomposition. IEEE Transactions on Ultrasonic, Ferroelectrics and Frequency Control, 53, 2121–2131.

    Google Scholar 

  41. Mazumder, S. (2017). Single-step and multiple-step forecasting in one-dimensional chirp signal using MCMC-based Bayesian analysis. Communications in Statistics - Simulation and Computation, 46, 2529–2547.

    MathSciNet  MATH  Google Scholar 

  42. Montgomery, H. L. (1990). Ten lectures on the interface between analytic number theory and harmonic analysis (vol. 196). Providence: American Mathematical Society.

    Google Scholar 

  43. Nandi, S., & Kundu, D. (2004). Asymptotic properties of the least squares estimators of the parameters of the chirp signals. Annals of the Institute of Statistical Mathematics, 56, 529–544.

    MathSciNet  MATH  Google Scholar 

  44. Nandi, S., & Kundu, D. (2006). Analyzing non-stationary signals using a cluster type model. Journal of Statistical Planning and Inference, 136, 3871–3903.

    MathSciNet  MATH  Google Scholar 

  45. Nandi, S., Kundu, D., & Grover, R. (2019). Estimation of parameters of multiple chirp signal in presence of heavy tailed errors.

    Google Scholar 

  46. O’Shea, P. (2010). On refining polynomial phase signal parameter estimates. IEEE Transactions on Aerospace, Electronic Syatems, 4, 978–987.

    Google Scholar 

  47. Pelag, S., & Porat, B. (1991). Estimation and classification of polynomial phase signals. IEEE Transactions on Information Theory, 37, 422–430.

    MathSciNet  Google Scholar 

  48. Richards, F. S. G. (1961). A method of maximum likelihood estimation. Journal of Royal Statistical Society Series B, 23, 469–475.

    MathSciNet  MATH  Google Scholar 

  49. Pincus, M. (1968). A closed form solution of certain programming problems. Operation Research, 16, 690–694.

    MathSciNet  MATH  Google Scholar 

  50. Rihaczek, A. W. (1969). Principles of high resolution radar. New York: McGraw-Hill.

    MATH  Google Scholar 

  51. Robertson, S. D. (2008). Generalization and application of the linear chirp. Ph.D. Dissertation, Southern Methodist University, Department of Statistical Science.

    Google Scholar 

  52. Robertson, S. D., Gray, H. L., & Woodward, W. A. (2010). The generalized linear chirp process. Journal of Statistical Planning and Inference, 140, 3676–3687.

    MathSciNet  MATH  Google Scholar 

  53. Saha, S., & Kay, S. M. (2002). Maximum likelihood parameter estimation of superimposed chirps using Monte Carlo importance sampling. IEEE Transactions on Signal Processing, 50, 224–230.

    Google Scholar 

  54. Seber, G. A. F., & Wild, C. J. (1989). Nonlinear regression. New York: Wiley.

    MATH  Google Scholar 

  55. Ticahvsky, P., & Handel, P. (1999). Multicomponent polynomial phase signal analysis using a tracking algorithm. IEEE Transactions on Signal Processing, 47, 1390–1395.

    Google Scholar 

  56. Volcker, B., & Ottersten, B. (2001). Chirp parameter estimation from a sample covariance matrix. IEEE Transactions on Signal Processing, 49, 603–612.

    Google Scholar 

  57. Wang, J. Z., Su, S. Y., & Chen, Z. (2015). Parameter estimation of chirp signal under low SNR. Science China: Information Sciences, 58. Article ID 020307.

    Google Scholar 

  58. Wang, P., & Yang, J. (2006). Multicomponent chirp signals analysis using product cubic phase function. Digital Signal Processing, 16, 654–669.

    Google Scholar 

  59. Wang, Y., & Zhou, Y. G. T. (1998). On the use of high-order ambiguity function for multi-component polynomial phase signals. Signal Processing, 5, 283–296.

    MATH  Google Scholar 

  60. Wu, C. F. J. (1981). Asymptotic theory of the nonlinear least squares estimation. Annals of Statistics, 9, 501–513.

    MathSciNet  MATH  Google Scholar 

  61. Xinghao, Z., Ran, T., & Siyong, Z. (2003). A novel sequential estimation algorithm for chirp signal parameters. In IEEE Conference in Neural Networks and & Signal Processing, Nanjing, China (pp. 628–631). Retrieved Dec 14–17, 2003

    Google Scholar 

  62. Yaron, D., Alon, A., & Israel, C. (2015). Joint model order selection and parameter estimation of chirps with harmonic components. IEEE Transactions on Signal Processing, 63, 1765–1778.

    MathSciNet  MATH  Google Scholar 

  63. Yang, P., Liu, Z., & Jiang, W.-L. (2015). Parameter estimation of multicomponent chirp signals based on discrete chirp Fourier transform and population Monte Carlo. Signal, Image and Video Processing, 9, 1137–1149.

    Google Scholar 

  64. Zhang, H., Liu, H., Shen, S., Zhang, Y., & Wang, X. (2013). Parameter estimation of chirp signals based on fractional Fourier transform. The Journal of China Universities of Posts and Telecommunications, 20(Suppl. 2), 95–100.

    Google Scholar 

  65. Zhang, H., & Liu, Q. (2006). Estimation of instantaneous frequency rate for multicomponent polynomial phase signals. In ICSP2006 Proceedings (pp. 498–502). https://doi.org/10.1109/ICOSP.2006.344448.

  66. Zhang, K., Wang, S., & Cao, F. (2008). Product cubic phase function algorithm for estimating the instantaneous frequency rate of multicomponent two-dimensional chirp signals. In 2008 Congress on Image and Signal Processing. https://doi.org/10.1109/CISP.2008.352.

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Authors and Affiliations

  1. Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, New Delhi, Delhi, India

    Swagata Nandi

  2. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Debasis Kundu

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  1. Swagata Nandi
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  2. Debasis Kundu
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Correspondence to Swagata Nandi .

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Nandi, S., Kundu, D. (2020). Chirp Signal Model. In: Statistical Signal Processing. Springer, Singapore. https://doi.org/10.1007/978-981-15-6280-8_9

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