Abstract
In this paper of the series on multi-resolution Fourier analysis, labeled NY-MFA, it is shown that the problem of finite observation and its detrimental consequences on amplitude resolution are eliminated. Obscuring and distorting effects of implicit windowing are suppressed without altering already provided frequency resolution in excess of Gabor–Heisenberg limit. Weak, virtual or spurious spectral lines are detected. Easier and fine frequency estimations are provided. Proposed analysis opens promising perspectives free of finite observation effects helping, by the way, to avoid misleading interpretations and diagnosis errors.



Similar content being viewed by others
References
Kay, S.K., Marple, S.L.: Spectrum Analysis-A modern perspective. Proc. IEEE 69(11), 1380–1419 (1981)
Haris, F.J.: On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66(1), 51–83 (1978)
Webster, R.J.: Leakage regulation in the discrete Fourier transform spectrum. Proc. IEEE 68(10), 1339–1341 (1980)
Yahya Bey, N.: Multi-resolution Fourier analysis, Part I : fundamentals. Int. J. Commun. Netw. Syst. Sci. 4(6), 364–371 (2011)
Yahya Bey, N.: Multi-resolution Fourier analysis, Part II : missing signal recovery and observation results. Int. J. Commun. Netw. Syst. Sci. 5(1), 28–36 (2012)
Yahya Bey, N.: Multi-resolution Fourier analysis: extraction and missing signal recovery of short buried signals in noise. Signal Image Video Process. 8(8), 1483–1495 (2014)
Yahya Bey, N.: Multi-resolution Fourier analysis: time-frequency resolution in excess of Gabor-Heisenberg limit. Signal Image Video Process. 8(4), 765–778 (2014)
Terhardt, E.: Fourier transformation of time signals: conceptual revision. Acustica 57, 242–256 (1985)
Candan, C.: A method for fine resolution frequency estimation from three DFT samples. IEEE Signal Process. Lett. 8(6) (2011)
Acknowledgments
The author would like to thank anonymous reviewers for their suggestions and helpful comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yahya Bey, N. Multi-resolution Fourier Analysis: achieved high resolutions with suppressed finite observation effects. SIViP 10, 711–718 (2016). https://doi.org/10.1007/s11760-015-0799-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11760-015-0799-8