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Original Articles

Deconvolution by Cepstral Transformation

Invited Paper

(Member)
Pages 515-532 | Received 30 Apr 1982, Published online: 10 Jul 2015

REFERENCES

  • Bayless (J W) & Brigham (E O). Application of the Kalman Filter. Geophysics, 35, 1: 1970; 2–23.
  • Berkhout (A J). Least Squares Inverse Filtering and Wavelet Deconvolution. Geophysics, 42, 7; 1977; 1369.
  • Bogert (B P), Healey (M J) & Tukey (J W). The Quefrency Analysis of Time Series for Echoes; Cepstrum, Pseudoautocovariance, Cross-cepstrum and saphe Cracking, Proc. Symp. on Time-Series Analysis, Ed. Rosenblatt (M). John Wiley, N.Y., 1963, 209–243.
  • Bogert (B P) & Ossanna (J F). The Heuristics of Cepstrum Analysis of a Stationary Complex Echoed Gaussian Signal in Stationary Gaussian Noise, IEEE Trans. IT-12, 3; 1966; 373–380.
  • Buhl (P), Stoffa (P L) & Bryan (G M). The Application of Homomorphic Deconvolution to Shallow-Water Marine Seismology. Part II: Real Data. Geophysics. 39, 4; 1974; 417–426.
  • Burg (J P). Maximum Entropy Spectral Analysis. 37th Meet SEG, Oklahama, 1967.
  • Burg (J P). Maximum Entropy Spectral Analysis, PhD Thesis, Stanford Univ., Palo Alto, Calif., 1975.
  • Buttkus (N). Homomorphic Filtering—Theory and Practice. Geophysical Prospecting. 23, 4; 1975; 712–748.
  • Compbell (G A) & Foster (R M). Fourier integrals for Practical Applications. Van Nostrand, Princeton. N.J., 1948, P 177
  • Charlier (C V L). Researches into the Theory of Probabilityl 1906. Lund.
  • Claerbout (J F) & Robinson (E A). A Short Note on the Error in Least-Squares Inverse Filtering. Geophysics. 29, 1; 1964; 118–120.
  • Clayton (R W) & Wiggins (R A). Source Shape Estimation and Deconvolution of Teleseismic Body Waves. Geophysics. J. Roy. Astr. Soc. 47, 1976; 151–177.
  • Crump (N D). A Kalman Filter Approach to the Deconvolution of Seismic Signals. Geophysics. 39, 1; 1974; 1–13.
  • Eliot (T S). Notes towards the Definition of Culture. 1948. Faber and Faber, London, P 86.
  • Fisz (M). Probability Theory and Mathematical Statistics. 1963. J. Wiley, NY, 64–67.
  • Fryer (G J), Odegard (M E) & Sutton (G H). Deconvolution and Spectral Estimation Using Final Prediction Error. Geophysics 40, 3; 1975; 411–425.
  • Galbraith (J N). Prediction Error as a Criterion for Operator Length. Geophysics. 36, 2; 1971; 261–265.
  • Golay (M J E). Sieves for Low Autocorrelation Binary Sequences. IEEE Trans. IT-23, 1; 1977; 43–51.
  • Green (C D). Integral Equation Methods. 1969. Nelson, London P 81–114.
  • Hoheiscl (G) & Tropper (A M). Integral Equations. 1967. Nelson, London, P 44–48.
  • Kailath (T). A View of Three Decades of Linear Filtering Theory. IEEE Trans. IT-20, 2; 1974; 158.
  • Kemerit (R C) & Childers (D G). Signal Dectection and Extraction by Cepstrum Techniques. IEEE Trans. IT-18, 6; 1972; 745–759.
  • Kenney (J F) & Keeping (E S). Mathematics of Statistics, Part II, 1965, Affiliated East-West Press, New Delhi, P 77–80, P 107–108.
  • Khattri (K) & Sharma (R). Estimation of the Source Time Function of the 1967 Koyna Earthquake by Log-Exp Filtering of Long Period Seismograms. Bull. I.S.E.T. 18, 4; 1981; 143–156.
  • Kolmogorov (A N). Sur 1' Interpolation et Extrapolation des Suites Stationnaires. C.R. Acad Sci. Paris. 208, 1939; 2043–2045.
  • Kopec (G E), Oppenheim (A V) & Tribolet (J M). Speech Analysis by Homomorphic Prediction. IEEE Trans. ASSP-23, 1; 1977; 40–49.
  • Lee (Y W). Statistical Theory of Communication. 1966. J. Wiley, N.Y. P 93–96, P 371–374.
  • Lines (L R) & Ulrych (T J). The Old and the New in Seismic Deconvolution and Wavelet Estimation. Geophysical Prospecting. 25, 3; 1977; 512–540.
  • Meidell (N S). Short note—Deterministic Deconvolution Operators—3-point or 4-point? Geophysics. 37, 6; 1972; 1039–1042.
  • Muth (E J). Transform Methods with Applications to Engineering and Operations Research. 1977. Prentice-Hall, Englewood Cliffs. N.J. 356–364.
  • Noll (A M). Cepstrum Pitch Determination. J. Acoust. Soc. Am. 41, 2; 1967; 293–309.
  • Oppenheim (A V). Superposition in a Class of Nonlinear Systems. Research Lab. of Electronics, M.I.T., Tech. Rep. 432. 1965; 62.
  • Oppenheim (A V). Generalized Superposition. Information & Control. 11,5,6; 1967; 528–536.
  • Oppenheim (A V), a. Generalized Linear Filtering. In Gold (B) & Rader (C M). Digital Processing of Signals, 1969. McGraw-Hill, N.Y., 233–264.
  • Oppenheim (A V). b. A Speech Analysis-Synthesis System Based on Homomorphic Filtering. J. Acoust. Soc. Amer. 45, 2; 1969; 458–465.
  • Oppenheim (A V), Kopec (G E) & Tribolet (J M). Signal Analysis by Homomorphic Prediction. IEEE Trans. ASSP-24, 4; 1976; 327 -332.
  • Oppenheim (A V) & Schafer (R W). Homomorphic Analysis of Speech. IEEE Trans. AU-16, 2; 1968; 221–226.
  • Oppenheim (A V) & Schafer (R W). Digital Signal Processing. 1975. Pi entice-Hall, Englewood Cliffs, N.J., P 480–531.
  • Oppenheim (A V), Schafer (R W) & Stockham (T G Jr.). Nonlinear Filtering of Multiplied and Convolved Signals. Proc. IEEE. 56, 8; 1968; 1264–1291.
  • Oppenheim (A V) & Weinstein (C J). Effects of Finite Register Length in Digital Filtering and Fast Fourier Transform. Proc. IEEE. 60, 8; 1972; 957–976.
  • Otis (R M) & Smith (R B). Homomorphic Deconvolution by Log-Spectral Averaging. Geophysics. 42, 6; 1977; 1146.
  • Papoulis (A). Signal Analysis. 1977. McGraw-Hill, N.Y. P 25, P 404.
  • Peacock (K L) & Treitel (S). Predictive Deconvolution; Theory and Practice. Geophysics. 34, 2; 1969; 155–169.
  • Pfleuger (J). Spectra of Water Reverberations for Primary and Multiple Reflections. Geophysics. 37, 5; 1972; 788–796.
  • Poisson (S D). Sur la Distribution de la Chaleur dans les Corps Solides. J. Ec. R. Polytech., Ser. I. 19, 1823; 1–162.
  • Prabhakar (J C), & Gupta (S C). Separation of Rayleigh and Poisson Density Functions through Homomorphic Filtering. Nat. Electronics Conf., 1970, 605–610.
  • Regan (R D) & Hinze (W J). The Effect of Finite Data Length in the Spectral Analysis of Ideal Gravity Anomalies. Geophysics. 41, 1; 1976; 44–55.
  • Rice (R B). Inverse Convolution Filters. Geophysics. 27, 1; 1962; 4–18.
  • Robinson (E A). Predictive Decomposition of Time Series with Applications to Seismic Exploration. PhD Thesis, MIT, Cambridge. 1964, P, 252 Also in Geophysics. 32, 3; 1967; 418–484.
  • Robinson (E A). Predictive Deconvolution of Seismic Traces. Geophysics. 22, 4; 1957; 767–778.
  • Robinson (E A). Dynamic Predictive Deconvolution. Geophysical Prospecting. 23, 4; 1975; 780–798.
  • Rom (R). On the Cepstrum of Two-dimensional Functions. IEEE Trans. IT-21, 2; 1975; 214–217.
  • Schafer (R W). Echo Removal by Discrete Generalized Linear Filtering. Research lab. of Electronics, MIT. Tech. Rep. 466, 1969.
  • Schafer (R W) & Rabiner (I R). System for Automatic Formant Analysis of Voiced Speech. J. Acoust. Soc. Am. 47, 2; 1970; 634–648.
  • Schwarz (H A). Zur Integration der Partiellen Differential-Gleichung. Z. Reine Angewandte Math., 1872, 218–254.
  • Silvia (M T) & Robinson (E A). Dsconvolution of Geophysical Time Series in the Exploration for Oil and Natural Gas, 1979. Elsevier, Amsterdam. P 92–93, P 111.
  • Sinton (J B), Ward (R W) & Watkins (J S). Suppression ot Long-Delay Multiple Reflections by Predictive Deconvolution. Geophysics. 43, 7; 1978; 1352.
  • Stockham (T J Tr), Cannon (T M) & Ingebrctsen (R B). Blind Deconvolution through Digital Signal Processing. Proc. IEEE 63, 4; 1975; 678–692.
  • Stoffa (P L), Buhl (P) & Bryan (G M). The Application of Homomorphic Deconvolution to Shallow-Water Marine Seismology-Part I: Models, Geophysics. 39, 4; 1974; 401–416.
  • Szego (G). Ein Grenzwertsatz Uber die Toeplitzschen Determinaten einer Reelen Positiven Funktion, Math. Ann. 76 1915; 490–503.
  • Thomas (J B). An Introduction to Statistical Communication Theory. 1969. John Wiley, N.Y. 386–400, 143.
  • Titchmarsh (E C). Introduction to the Theory of Fourier Integrals. 1950. Clarendon Press, Oxford, P 96–118.
  • Treitel (S) & Robinson (E A). Deconvolution—Homomorphic or Predictive? IEEE Trans. GE-15, 1; 1977; 11–13.
  • Tretiak (O J) & Eisenstein (B A). Separator Functions for Homomorphic Filtering. IEEE Trans. ASSP-24, 5; 1976; 359–364.
  • Ulrych (T J). Application of Homomorphic Deconvolution to Seismology. Geophysics. 36, 4; 1971; 650–660.
  • Ulrych (T J) & Bishop (T). Maximum Entropy Spectral Analysis and Autoregressive Decomposition. Rev. Geophys. 13, 1975; 183–200.
  • Ulrych (T J), Jensen (O G), Ellis (R M) & Somerville (P G). Homomorphic Deconvolution of Some Teleseismic Events. Bull. Seism. Soc. Am. 62, 5; 1972; 1269–1281.
  • Vakman (D E). Sophisticated Signals and the Uncertainty Principles in Radar. Ed. Jacobs (E). 1968, Springer-Verlag, Berlin, P 16–17, 62–72, 6–9, 126–224.
  • Wang (R J). Adaptive Predictive Deconvolution of Seismic Data. Geophysical Prospecting. 25, 2; 1977; 342–381.
  • Whalen (A D). Detection of Signals in Noise. 1971. Academic Press, N.Y. P 246–258, 113–118.

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