Abstract
A method for approximation of an arbitrary continuous function in the neighborhood of a given point by complex exponential functions (exponentials) is described. The method is similar to the Taylor series to the effect that approximation is performed by the derivatives at the given point. Determination of parameters of the exponentials is made on the basis of a modified Prony’s method. It is shown that the method makes it possible to simulate the local behavior of periodic and quasiperiodic processes more effectively than a Taylor series. An algorithm for estimating the instantaneous parameters of the single-component quasiperiodic continuous signals is obtained. The relation to a known energy separation algorithm (ESA) is shown. A separate algorithm for discrete signals by using finite differences is obtained. The applicability of the algorithm for practical analysis of discrete signals with consideration of the influence of additive noise on the accuracy of the parameter estimates is investigated. Experimental comparison of the algorithm with the known methods of estimating instantaneous parameters on the basis of the Prony’s method and ESA is performed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Marple, S.L., Tsifrovoi spektral’nyi analiz i ego prilozheniya (Digital Spectral Analysis with Applications), Prentice Hall, 1987; Moscow: Mir, 1990.
Boashash, B., Estimating and interpreting the instantaneous frequency of a signal, Proc. IEEE, 1992, vol. 80,no. 4, pp. 519–568.
Azarov, E., Vashkevich, M., and Petrovsky, A., Instantaneous harmonic representation of speech using multicomponent sinusoidal excitation, Proc. 14th Ann. Conf. Int. Speech Commun. Assoc. (INTERSPEECH-2013), Lyon, 2013, pp.1–5.
Abe, T. and Honda, N., Sinusoidal model based on instantaneous frequency attractors, IEEE Trans. Audio, Speech, and Language Proc., 2006, vol. 14, pp. 1292–1300.
Maragos, P., Kaiser, J.F., and Quatieri, T.F., Energy separation in signal modulations with application to speech analysis, IEEE Trans. Signal Proc., 1993, vol. 41, pp. 3024–3051.
Dimitriadis, D., Potamianos, A., and Maragos, P., A comparison of the squared energy and Teager-Kaiser operators for short-term energy estimation in additive noise, IEEE Trans. Signal Proc., 2009, vol. 57, pp. 2569–2581.
Kaiser, J.F., On a simple algorithm to calculate the “energy” of a signal, Proc. IEEE ICASSP-90, Albuquerque, New Mexico, 1990, pp. 381–384.
Dimitriadis, D. and Maragos, P., Continuous energy demodulation methods and application to speech analysis, Speech Commun., 2006, vol. 48, pp. 819–837.
Litvin, Y., Cohen, I., and Chazan, D., Monoural speech/music source separation using discrete energy separation algorithm, Signal Proc., 2010, vol. 90, pp. 3147–3163.
Maragos, P., Potamianos, A., and Santhanam, B., Instantaneous energy operators: Applications to speech processing and communications, Proc. IEEE Workshop on Nonlinear Signal and Image Proc., Thessaloniki, Greece, 1995.
Fertig, L.B. and McClellan, J.H., Instantaneous frequency estimation using linear prediction with comparisons to the DESAs, IEEE Signal Proc. Lett., 1996, vol. 3, no. 2, pp. 54–56.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.S. Azarov, M.I. Vashkevich, A.A. Petrovsky, 2015, published in Avtomatika i Vychislitel’naya Tekhnika, 2015, No. 2, pp. 65–80.
About this article
Cite this article
Azarov, E.S., Vashkevich, M.I. & Petrovsky, A.A. Estimation of the instantaneous signal parameters using a modified Prony’s method. Aut. Control Comp. Sci. 49, 110–121 (2015). https://doi.org/10.3103/S0146411615020029
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0146411615020029