A property of the elementary symmetric functions on the frequencies of sinusoidal signals

Signal Processing

Volumn 89, Issue 5, 2009, Pages 765-777

  Coluccio, Loredana ^a   Eisinberg, Alfredo ^a   Fedele, Giuseppe ^a  

^a UNIVERSITY OF CALABRIA   (Italy)

Author keywords

Elementary symmetric functions; Frequency estimation; Least squares; Multi sine wave signal

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; ELECTRIC NETWORK ANALYSIS; ESTIMATION; FUNCTIONS; LINEAR SYSTEMS; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; REAL TIME SYSTEMS; TIME DOMAIN ANALYSIS;

DATA RECORDS; DERIVATIVE METHODS; ELEMENTARY SYMMETRIC FUNCTIONS; EXACT FORMULAS; FREQUENCY DOMAINS; LABORATORY EXPERIMENTS; LEAST-SQUARES; LEAST-SQUARES ESTIMATIONS; MEASUREMENT NOISE; MULTI-SINE WAVE SIGNAL; MULTIPLE INTEGRALS; PARAMETERS ESTIMATIONS; SINUSOIDAL COMPONENTS; SINUSOIDAL SIGNALS; TIME DOMAINS; TIME-VARYING FILTERS; UNIFORM SAMPLINGS;

FREQUENCY ESTIMATION;

EID: 58849158249     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2008.10.021     Document Type: Article

References (43)

1. Wu J., Long J., and Wang J. High-accuracy, wide-range frequency estimation methods for power system signals under nonsinusoidal conditions. IEEE Trans. Power Delivery 20 1 (2005) 366-374
2. So H.C., Chan K.W., Chan Y.T., and Ho K.C. Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses. IEEE Trans. Signal Process. 53 7 (2005) 2290-2305
3. Chan K.W., and So H.C. Accurate frequency estimation for real harmonic sinusoids. IEEE Signal Process. Lett. 11 7 (2004) 609-612
4. So H.C., and Chan K.W. A generalized weighted linear predictor frequency estimation approach for a complex sinusoid. IEEE Trans. Signal Process. 54 4 (2006) 1304-1315
5. Abeysekera S.S. Efficient frequency estimation using the pulse-pair method at various lags. IEEE Trans. Comm. 54 9 (2006) 1542-1546
6. Klein J.D. Fast algorithms for single frequency estimation. IEEE Trans. Signal Process. 54 5 (2006) 1762-1770
7. El-Shafey M.H., and Mansour M.M. Application of a new frequency estimation technique to power systems. IEEE Trans. Power Delivery 21 3 (2006) 1045-1053
8. Trapero J.R., Sira-Ramirez H., and Batlle V.F. An algebraic frequency estimator for a biased and noisy sinusoidal signal. Signal Processing 87 6 (2007) 1188-1201
9. Pradhan A.K., Routray A., and Basak A. Power system frequency estimation using least mean square technique. IEEE Trans. Power Delivery 20 3 (2005) 1812-1816
10. Leven A., Kaneda N., Koc U.V., and Chen Y.K. Frequency estimation in intradyne reception. IEEE Photonics Technol. Lett. 19 6 (2007) 366-368
11. Hackman C., Levine C., Parker J., Piester T.E., Becker D., and Becker J. A straightforward frequency-estimation technique for GPS carrier-phase time transfer. IEEE Trans. Ultrasonics Ferroelectrics Frequency Control 53 9 (2006) 1570-1583
12. Klapuri A.P. Multiple fundamental frequency estimation based on harmonicity and spectral smoothness. IEEE Trans. Speech Audio Process. 11 6 (2003) 804-816
13. Östlund N., Yu J., and Karlsson J.S. Improved maximum frequency estimation with application to instantaneous mean frequency estimation of surface electromyography. IEEE Trans. Biomedical Eng. 51 9 (2004) 1541-1546
14. Zhang Q., and Brown L.J. Noise analysis of an algorithm for uncertain frequency identification. IEEE Trans. Automat. Control 51 1 (2006) 103-110
15. Stoica P. List of references on spectral line analysis. Signal Processing 31 3 (1993) 329-340
16. M.H. El-Shafey, Effect of the sampling time on the accuracy of estimating the frequencies of multiple sinusoids, in: The 2006 International Conference on Computer Engineering and Systems, 2006, pp. 324-328.
17. Fliess M., and Sira-Ramirez H. An algebraic framework for linear identification. ESAIM Control Optim. Calculus Variations 9 (2003) 151-168
18. Fliess M., Mboup M., Mounier H., and Sira-Ramirez H. Questioning some paradigms of signal processing via concrete examples. In: Sira-Ramirez H., and Silva-Navarro G. (Eds). Algebraic Methods in Flatness, Signal Processing and State Estimation (2003), Editorial Lagares, México 1-21
19. A. Bonaventura, L. Coluccio, G. Fedele, Frequency estimation of multi-sinusoidal signal by multiple integrals, in: 2007 IEEE International Symposium on Signal Processing and Information Technology, 2007, pp. 564-569.
20. M. Fliess, H. Sira-Ramirez, Closed-loop parametric identification for continuous-time linear systems, in: H. Garnier, L. Wang (Eds.), Continuous-Time Model Identification from Sampled Data, Springer, Berlin, 2008.
21. Fliess M. Analyse non standard du bruit. C. R. Acad. Sci. Paris Ser. I 342 (2006) 792-802
22. M. Fliess, Critique du rapport signal à bruit en théorie de l'information, Technical Report INRIA, no. 00195987, 11 December 2007.
23. Eisinberg A., and Fedele G. A property of the elementary symmetric functions. Calcolo 42 (2005) 31-36
24. Eisinberg A., and Fedele G. On the inversion of the Vandermonde matrix. Appl. Math. Comput. 174 (2006) 1384-1397
25. Coluccio L., Eisinberg A., and Fedele G. A Prony-like method for non-uniform sampling. Signal Processing 87 10 (2007) 2484-2490
26. Young D.M., and Gregory R.T. A Survey of Numerical Mathematics vol. I (1972), Addison-Wesley, Reading, MA
27. McNamee J.M. A 2002 update of the supplementary bibliography on roots of polynomials. J. Appl. Math. Comput. 142 (2002) 433-434
28. Kumaresan R. On the zeros of the linear prediction-error filter for deterministic signals. IEEE Trans. Acoust. Speech Signal Process. 31 1 (1983) 217-220
29. Quinn B.G., and Hannan E.J. The Estimation and Tracking of Frequency (2001), Cambridge University Press, Cambridge
30. Li Y., Liu K.J.R., and Razavilar J. Improved parameter estimation schemes for damped sinusoidal signals based on low-rank Hankel approximation. IEEE Trans. Signal Process. 45 (1997) 481-487
31. Lobos T., Kozina T., and Koglin H.J. Power system harmonics estimation using linear least squares method and SVD. IEE Proc. Gener. Transm. Distrib. 148 6 (2001) 567-572
32. Leonowicz Z., Lobos T., and Rezmer J. Advanced spectrum estimation methods for signal analysis in power electronics. IEEE Trans. Industrial Electr. 50 3 (2003) 514-519
33. Johansson R. Identification of continuous-time models. IEEE Trans. Signal Process. 42 4 (1994) 887-897
34. M. Gilson, H. Garnier, P. Van den Hof, Instrumental variable methods for continuous-time model identification in closed-loop, in: Proceedings of the 2004 American Control Conference, 2004, pp. 2846-2851.
35. R. Pintelon, J. Schoukens, P. Guillaume, Continuous-time noise modelling from sampled data, in: IMTC-Instrumentation and Measurement Technology Conference, 2006, pp. 1010-1014.
36. M. Mboup, Parameter estimation via differential algebra and operational calculus, Manuscript, 2006. Available at: 〈http://hal.inria.fr/inria-00138294〉.
37. N.J. Higham, A survey of componentwise perturbation theory in numerical linear algebra, in: W. Gautschi (Ed.), Mathematics of Computation 1943-1993: A Half Century of Computational Mathematics, vol. 48, 1994, pp. 49-77.
38. Mackisack M.S., Osborne M.R., and Smyth G.K. A modified Prony algorithm for estimating sinusoidal frequencies. J. Statist. Comput. Simulation 49 (1994) 111-124
39. Xia X. Global frequency estimation using adaptive identifiers. IEEE Trans. Automat. Control 47 7 (2002) 1188-1193
40. Bobtsov A.A. New approach to the problem of globally convergent frequency estimator. Internat. J. Adaptive Control Signal Process. 22 3 (2008) 306-317
41. D.E. Knuth, The Art of Computer Programming, vol. 1, second ed., Addison-Wesley, Reading, MA, 1973.
42. M. Petkovšek, H.S. Wilf, D. Zeilberger, A = B, AK Peters, Wellesley, 1996.
43. Luke Y.L. The Special Functions and Their Approximations vol. I (1969), Academic Press, New York