Multi-Resolution Fourier Analysis Part II: Missing Signal Recovery and Observation Results

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DOI: 10.4236/ijcns.2012.51004   PDF   HTML   XML   3,902 Downloads   6,747 Views   Citations

Abstract

In this paper, we report application procedures and observed results of multi-resolution Fourier analysis proposed in the first part of this series. Missing signal recovery derived from multi-resolution theory is developed. It is shown that multi-resolution Fourier analysis enhances dramatically performances of Fourier spectra suffering limitations traced to implicit time windowing. Observed frequency resolutions, improvement of frequency estimations, contraction of spectral leakage and recovery of missing parts of finite duration signals are in accordance with theoretical predictions.

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N. Yahya Bey, "Multi-Resolution Fourier Analysis Part II: Missing Signal Recovery and Observation Results," International Journal of Communications, Network and System Sciences, Vol. 5 No. 1, 2012, pp. 28-36. doi: 10.4236/ijcns.2012.51004.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] N. Yahya Bey, “Multi-Resolution Fourier Analysis Part I: Fundamentals”, International Journal of Communications, Network and System Sciences, Vol. 4, No. 6, 2011, pp. 364-371. doi:10.4236/ijcns.2011.46042
[2] S. M. Kay and S. L. Marple, “Spectrum Analysis-A Modern Perspective,” Proceedings of the IEEE, Vol. 69, No. 11, 1981. doi:10.1109/PROC.1981.12184
[3] E. Terhardt, “Fourier Transformation of Time Signals: Conceptual Revision,” Acustica, Vol. 57, 1985, pp. 242-256.
[4] D. L. Donoho and P. H. Stark, “Uncertainty Principles and Signal Recovery,” SIAM Journal on Applied Mathematics, Vol. 49, No. 3, 1989, pp. 906-931. doi:10.1137/0149053

  
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