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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 6
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Original Articles

Sampling theorem and multi-scale spectrum based on non-linear Fourier atoms

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Pages 903-919 | Received 01 Apr 2009, Accepted 07 May 2009, Published online: 05 Aug 2009

References

  • Fefferman , C and Stein , EM . 1972 . Hp spaces of several variables . Acta Math. , 129 : 137 – 193 .
  • Gel'fand , IM and Shilov , GE . 1967 . Generalized Functions , Vol. 2 , New York : Academic Press .
  • Bedrosian , E . 1963 . A product theorem for Hilbert transform . Proc. IEEE , 51 : 868 – 869 .
  • Boashash , B . 1992 . Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals . Proc. IEEE , 80 : 417 – 430 .
  • Cohen , L . 1995 . Time-frequency Analysis , Englewood Cliffs, NJ : Prentice-Hall .
  • Picinbono , B . 1997 . On instantaneous amplitude and phase of signals . IEEE Trans. Signal Process. , 45 : 552 – 560 .
  • Qian , T . 2006 . Unit analytic signals and harmonic measures . J. Math. Anal. Appl. , 314 : 526 – 536 .
  • Chen , QH , Li , LQ and Qian , T . 2007 . “ Time-frequency aspects of nonlinear fourier atoms ” . In in Wavelet Analysis and Applications , 287 – 297 . Basel : Birkäuser .
  • Chen , QH , Li , LQ and Qian , T . 2006 . Two families of unit analytic signals with nonlinear phase . Physica D , 221 : 1 – 12 .
  • Qian , T , Chen , QH and Li , LQ . 2005 . Analytic unit quadrature signals with nonlinear phase . Physica D , 203 : 80 – 87 .
  • Qian , T . 2005 . Characterization of boundary values of functions in Hardy spaces with applications in signal analysis . J. Integral Equ. Appl. , 17 ( 2 ) : 159 – 198 .
  • Nuttall , AH . 1966 . On the quadrature approximation to the Hilbert transform of modulated signals . Proc. IEEE Lett. , 54 : 1458 – 1459 .
  • Daubechies , I . 1992 . Ten Lectures on Wavelets , CBMS 61 Philadelphia : SIAM .
  • Huang , NE , Shen , Z , Long , SR , Wu , ML , Shih , HH , Zheng , Q , Yen , N , Tung , CC and Liu , HH . 1998 . The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis . Proc. R. Soc. London. A , 454 : 903 – 995 .
  • Chen , QH , Huang , NE , Riemenschneider , S and Xu , Y . 2006 . A B-spline approach for emperical mode decomposition . Adv. Comput. Math. , 24 : 171 – 195 .
  • Lund , J and Bowers , K . 1992 . Sinc methods for quadrature and differential equations , Philadelphia : SIAM .
  • Kou , KI and Qian , T . 2005 . Sinc function theory with the several complex variables setting . Acta Math. Sin. , 25 ( 4 ) : 741 – 754 .
  • Cooley , JW and Tukey , JW . 1965 . An algorithm for the machine calculation of complex Fourier series . Math. Comput. , 19 : 297 – 301 .
  • Mallat , S . 1999 . A Wavelet Tour of Signal Processing , 2 , Amsterdam : Academic Press .

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