위상만을 이용한 신호복원의 유일성 판단법

Uniqueness Criteria for Signal Reconstruction from Phase-Only Data

  • 이동욱 (정회원, 동국대 공대 전기공학과) ;
  • 김영태 (정회원, 동국대 전기공학과)
  • 발행 : 2001.02.01

초록

In this paper, we propose an alternate method for determining the uniqueness of the reconstruction of a complex sequence from its phase. Uniqueness constraints could be derived in terms of the zeros of a complex polynomial defined by the DFT of the sequence. However, rooting of complex polynomials of high order is a very difficult problem. Instead of finding zeros of a complex polynomial, the proposed uniqueness criteria show that non-singularity of a matrix can guarantee the uniqueness of the reconstruction of a complex sequence from its phase-only data. It has clear advantage over the rooting method in numerical stability and computational time.

키워드

참고문헌

  1. A. Papoulis, 'A new algorithm in spectral analysis and band-limited extrapolation,' IEEE Transactions on Circuits and Systems, vol. 22, no. 9, pp. 735-742, September 1975 https://doi.org/10.1109/TCS.1975.1084118
  2. M. H. Hayes, J. S. Lim, and A. V. Oppenheim, 'Signal reconstruction from phase or magnitude,' IEEE Transactions on Acoustics, Speech, Signal Processing, vol. 28, no. 6, pp. 672-680, December 1980 https://doi.org/10.1109/TASSP.1980.1163463
  3. M. H. Hayes, 'The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,' IEEE Transactions on Acoustics, Speech, Signal Processing, vol. 30, no. 2, pp. 140-154, April 1982 https://doi.org/10.1109/TASSP.1982.1163863
  4. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, Prentice Hall, 1989
  5. D. Lee and J. H. McClellan, 'Extracting multiple frequencies from phase-only data,' IEEE Trans. AES, vol. 33, no. 3, pp. 795-801, July 1997 https://doi.org/10.1109/7.599246
  6. A. S. Householder, The Numerical Treatment of a Single Nonlinear Equation, McGraw-Hill, 1970
  7. M. J. Maron, Numerical Analysis, Macmillan, 1987
  8. W. S. McCormick and J. S. Lansford, 'Efficient parallel rooting of complex polynomials on the unit circle,' IEEE Trans. Signal Processing, vol. 39, no. 10, pp. 2347-2351, October 1991 https://doi.org/10.1109/78.91192
  9. C. Ma, 'Novel criteria of uniqueness for signal reconstruction from phase,' IEEE Trans. Signal Processing, vol. 39, no. 4, pp. 989-992, April 1991 https://doi.org/10.1109/78.80933
  10. J. R. Rice, The Approximation of Functions, vol. 1., Addison-Wesley, 1964