MEAN SQUARED ERRORS OF DOANE AND MODIFIED DOANE METHODS FOR BIN SIZE ESTIMATION
Recorded audio signals contain useful information. In the context of signal analysis, a trade-off between frequency estimation and time has to be made due to Heisenberg’s principle [2]. In this study, we use higher moments in attempting to obtain shorter windows of time applying a short time Fourier transform. The performance of these two estimators Doane and modified Doane has been studied based on their mean squared errors (MSE).
Heisenberg’s principle, Fourier transform, mean squared error, Doane and modified Doane methods.
Received: December 15, 2020; Accepted: December 29, 2020; Published: January 22, 2021
How to cite this article: Rhegie M. Caga-anan, Roberto N. Padua and Dennis A. Tarepe, Mean squared errors of Doane and modified Doane methods for bin size estimation, Far East Journal of Applied Mathematics 109(1) (2021), 67-79. 10.17654/AM109010067
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References[1] J. Fourier, Théorie analytique de la chaleur (The Analytical Theory of Heat), Encyclopaedia Britannica, 1822.[2] W. Heisenberg, Heisenberg Uncertainty Principle or Indeterminacy Principle, Encyclopaedia Britannica, 1927.[3] E. H. Kennard, Zur Quantenmechanik einfacher Bewegungstypen, Zeitschrift für Physik 44 (1927), 326-352. doi:10.1007/BF01391200.[4] B. Klemens, Modeling with Data: Tools and Techniques for Scientific Computing, Princeton University Press, Appendix M, 2008, pages 5 and 9.[5] H. Weyl, J. A. Wheeler, H. H. Goldstine and O. Veblen, Gruppentheorie und Quantenmechanik, Leipzig, S. Hirzel, 1928.