The Cepstrum: A Guide to Processing

Proceedings of the IEEE

Volumn 65, Issue 10, 1977, Pages 1428-1443

  Childers, Donald G ^a   Skinner, David P ^b   Kemerait, Robert C ^c  

^a UNIVERSITY OF FLORIDA   (United States)

^b NAVAL SURFACE WARFARE CENTER   (United States)

^c ENSCO INC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CEPSTRUM;

SIGNAL PROCESSING - REVIEWS;

SIGNAL THEORY;

EID: 0017542202     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/PROC.1977.10747     Document Type: Article

References (87)

1. B. P. Bogert, M. J. Healy, and J. W. Tukey, “The quefrency alanysis of time series for echoes: cepstrum, pseudo-autocovariance, cross-cepstrum, and saphe cracking,” in Time Series Analysis, M. Rosenblatt, Ed. New York: Wiley, 1963, Chap. 15, pp. 209–243.
2. B. P. Bogert and J. F. Ossanna “The heuristics of cepstrum analysis of a stationary complex echoed Gaussian signal in stationary Gaussian noise,” IEEE Trans. Inform. Theory, vol. IT-12, pp. 373–380, July 1966.
3. J. F. Bohme “The cepstrum as a generalized function,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 650–653, Sept., 1974.
4. D. Childers, “Composite signal decomposition techniques,” in Int. Conf. on Comm. (ICC), Seattle, WA, June 11–13, 1973, pp. 1–6.
5. D. E. Dudgeon “Existence of cepstra for two-dimensional rational polynomials,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-23, pp. 242–243, Apr. 1975.
6. J. C. Hassab “On the convergence interval of the power cepstrum,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 111–112, Jan. 1974.
7. J. C. Hassab and R. Boucher “A probabilistic analysis of time delay extraction by the cepstrum in stationary Gaussian noise,” IEEE Trans. Inform. Theory, vol. IT-22, pp. 444–454, July 1976.
8. — “Analysis of signal extraction, echo detection and removal by complex cepstrum,” J. Sound and Vibration, vol. 40, pp. 321–335, June 1975.
9. R. C. Kemerait, “Signal detection and extraction by cepstrum techniques,” Ph.D. Dissertation, University of Florida, 1971.
10. —, “Pseudo-heterodyning in the cepstral domain,” in 8th Ann. Southeastern Symp. System Theory, Apr. 26–27, 1976, pp. 37–41.
11. R. C. Kemerait and L. Balceda, “Signal detection and extraction by weighted cepstrum techniques,” in 1976 Southeastcon, Clemson University, IEEE Catalog No. 76 CH1059-5 Reg. 3, pp. 3B-1–3B-3, 1976.
12. R. Kemerait and D. G. Childers, “Composite signal decomposition by cepstrum techniques,” in IEEE Region 3 Convention Record, pp. K1-1–K1-4, 1972.
13. — “Signal detection and extraction by cepstrum techniques,” IEEE Trans. on Inform. Theory, vol. IT-18, pp. 745–759, Nov. 1972.
14. A. Noll, “The cepstrum and some close relatives,” in Signal Processing, J. W. R. Griffiths, P. L. Stocklin, and C. Van Schooneveld, Eds. London: Academic Press, 1973, pp. 11–22.
15. A. Oppenheim, “Superposition in a class of nonlinear systems,” M.I.T. Res. Lab. of Electronics, Cambridge, MA, Tech. Rep. 432 (Ph.D. dissertation), Mar. 31, 1965.
16. —, “Optimum homomorphic filters,” M.I.T. Res. Lab. of Electronics, Quarterly Progress Rep. no. 77, vol. XIII, Statistical Communication Theory, AD 615324, Apr. 15, 1965, pp. 248–260.
17. —, “Nonlinear filtering of convolved signals,” M.I.T. Res. Lab. of Electronics, Quarterly Progress Rep. no. 80, 1966.
18. —, “Generalized superposition,” Inform. Contr., vol. 11, pp. 528–536, Nov.–Dec, 1967.
19. A. V. Oppenheim, G. E. Kopec, and J. M. Tribolet, “Signal analysis sis by homomorphic prediction,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. ASSP-24, pp. 327–332, Aug. 1976.
20. A. V. Oppenheim, R. W. Schafer, and T. G. Stockham, Jr. “Nonlinear filtering of multiplied and convolved signals,” Proc. IEEE, vol. 56, pp. 1264–1291, Aug. 1968.
21. R. Rom, “On the cepstrum of two-dimensional functions,” IEEE Trans. on Inform. Theory, pp. 214–217, Mar. 1975.
22. R. W. Schafer, “Echo removal by discrete generalized linear filtering,” Ph.D. Dissertation, M.I.T., Cambridge, MA, 1968.
23. S. Senmoto, “Adaptive decomposition of composite signals in noise,” Ph.D. Dissertation, University of Florida, Gainesville, FL, 1971.
24. S. Senmoto and D. G. Childers, “Analysis of a composite signal by complex cepstrum and adaptive filter,” Trans. Inst. Elec. Comm. Engrs., (Japan), pt. A, pp. 9–16, 1972.
25. — “Adaptive decomposition of a composite signal of identical unknown wavelets in noise,” IEEE Trans. on Syst., Man, and Cybern., vol. SMC-2, pp. 59–66, Jan. 1972.
26. M. J. Shensa “Complex exponential weighting applied to homomorphic deconvolution,” Geophys. J. Roy. Astron. Soc., vol. 44, pp. 379–387, 1976.
27. D. P. Skinner, “Real-time composite signal decomposition,” Ph.D. Dissertation, University of Florida, Gainesville, FL, 1974.
28. D. P. Skinner and D. G. Childers, “The power, complex, and phase cepstra,” presented at 1975 Proc. Nat. Telecommun. Conf., Dec. 1975.
29. — “Real-time composite signal decomposition,” IEEE Trans. on Acoust., Speech, and Signal Processing, vol. ASSP-24, pp. 267–270, June 1976.
30. R. G. Smith “Cepstrum descrimination function,” IEEE Trans. Inform. Theory, vol. IT-21, pp. 332–334, May, 1975.
31. T. G. Stockham, Jr., T. M. Cannon, R. B. Ingebretsen “Blind deconvolution through digital signal processing,” Proc. IEEE, vol. 63, pp. 678–692, Apr. 1975. (Refer to for other related reports and Master's theses.)
32. P. L. Stoffa, P. Buhl, and G. M. Bryan “The application of homomorphic deconvolution to shallow-water marine seismology-Part I: Models,” Geophysics, vol. 39, no. 4, pp. 401–416, Aug. 1974.
33. — “Cepstrum aliasing and the calculation of the Hilbert transform,” Geophysics, vol. 39, no. 4, pp. 543–544, Aug. 1974.
34. A. J. Berkhout “On the minimum phase criterion of sampled signals,” IEEE Trans. Geosci. Electron, vol. GE-11, pp. 186–198, Oct. 1973.
35. W. H. Bakun and L. R. Johnson “The deconvolution of teleseismic P waves from explosions Milrow and Cannikin,” Geophys. J. Roy. Astron. Soc., vol. 34, pp. 321–342, 1973.
36. P. Buhl, P. L. Stoffa, and G. M. Bryan “The application of homomorphic deconvolution to shallow-water marine seismology-Part II: Real data,” Geophysics, vol. 39, no. 4, pp. 417–426, Aug. 1974.
37. T. Cohen “Source-depth determinations using spectral, pseudoautocorrelation and cepstral analysis,” Geophys. J. Roy. Astron. Soc., vol. 20, pp. 223–231, 1970.
38. pP phases from seven Pahute Mesa events,” Bull. Seismological Soc. Amer., vol. 65, no. 4, pp. 1029–1032, Aug. 1975.
39. P. O. Fjell “Use of the cepstrum method for arrival times extraction of overlapping signals due to multipath conditions in shallow water,” J. Acoust. Soc. Amer., vol. 59, no. 1, pp. 209–211, Jan. 1976.
40. O. S. Halpeny, “Epoch detection by cepstrum analysis,” Master's Thesis, University of Florida, Gainesville, FL, 1970.
41. R. Kemerait and D. G. Childers, “Detection of multiple echoes immersed in noise,” in Proc. 15th Midwest Symp. Circuit Theory, May 4–5, 1972 pp. 1–10.
42. —, “Decomposition of pulse-type data by cepstrum techniques,” 1973 IEEE Southeast Conf., Apr. 30, May 1–2, 1973, pp. F-4-1–F-4-4.
43. G. E. Kopec, A. V. Oppenheim, and J. M. Tribolet, “Speech analysis by homomorphic prediction,” submitted to IEEE Trans. Acoust., Speech and Signal Processing. (This paper is apparently an earlier version of [18].)
44. L. R. LeBlanc “Narrow-band sampled-data techniques for detection via the underwater acoustic communication channel,” IEEE Trans. Commun. Technol., vol. COM-17, pp. 481–488, Aug. 1969.
45. J. H. Miles, G. H. Stevens, and G. G. Leininger, “Analysis and correction of ground reflection effects in measured narrowband sound spectra using cepstral techniques,” presented at 90th Meeting of Acoust. Soc. Amer., Nov. 4–7, 1975.
46. S. K. Mitchell and N. R. Bedford, “Long range sensing of explosive source depths using cepstrum,” paper presented at 90th Meeting Acoust. Soc. Amer., Nov. 1975.
47. A. Noll “Short-time spectrum and ‘cepstrum’ techniques for vocal-pitch detection,” J. Acoust. Soc. Amer., vol. 36, pp. 296–302, Feb. 1964.
48. — “Cepstrum pitch determination,” J. Acoust. Soc. Am., vol. 41, no. 2, pp. 293–309, Feb. 1967.
49. — “Clipstrum pitch determination,” J. Acoust. Soc. Am., vol. 44, no. 6, pp. 1585–1591, Dec. 1968.
50. —, “Pitch determination of human speech by the harmonic product spectrum, the harmonic sum spectrum, and a maximum likelihood estimate,” in Computer Processing in Communications, J. Fox, Ed. Brooklyn, NY; Polytechnic, 1970, pp. 779–797.
51. A. Oppenheim “Speech analysis-synthesis system based on homomorphic filtering,” J. Acoust. Soc. Amer., vol. 45, no. 2, pp. 458–465, Feb. 1969.
52. A. Oppenheim and R. W. Schafer “Homomorphic analysis of speech,” IEEE Trans. Audio Electroacoust., vol. AU-16, pp. 221–226, June 1968.
53. J. Prabhakar and S. C. Gupta, “Separation of Rayleigh and Poisson density functions through homomorphic filtering,” Nat. Elec. Conf., pp. 605–610, Dec. 1970.
54. R. Schafer and L. R. Rabiner “System for automatic formant analysis of voiced speech,” J. Acoust. Soc. Amer., vol. 47, (Pt. 2), pp. 634–648, Feb. 1970.
55. S. Senmoto and D. G. Childers, “Decomposition of a composite signal of unknown wavelets in noise,” in Int. Conf. Comm. (ICC), 71C 28-COM, Montreal, Canada, 1971, pp. 5-14–5-19.
56. J. Tenold, D. H. Crowell, R. H. Jones, T. H. Daniel, D. F. McPherson, A. N. Popper “Cepstral and stationarity analysis of full-term and premature infants' cries,” J. Acoust. Soc. Amer., vol. 56, no. 3, pp. 975–980, Sept. 1974.
57. J. M. Tribolet, “A new phase unwrapping algorithm,” submitted to IEEE Trans. Acoust., Speech, and Signal Processing.
58. J. M. Tribolet, A. V. Oppenheim, and G. E. Kopec, “Deconvolution by homomorphic prediction,” submitted to Geophysics.
59. T. Ulrych “Application of homomorphic deconvolution to seismology,” Geophysics, vol. 36, no. 4, pp. 650–660, Aug. 1971.
60. T. Ulrych, O. G. Jensen, R. M. Ellis, and P. G. Sommerville “Homomorphic deconvolution of some teleseismic events,” Bull. Seismological Soc. Amer., vol. 62, no. 5, pp. 1253–1265, Mar. 1972.
61. D. J. H. Moore and D. J. Parker “On nonlinear filters involving transformation of the time variable,” IEEE Trans. Inform. Theory, vol. IT-19, pp. 415–422, July 1973.
62. B. Gold and C. M. Rader, Digital Processing of Signals. New York: McGraw-Hill, 1969.
63. L. R. Rabiner and B. Gold, Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
64. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
65. D. G. Childers and A. E. Durling, Digital Filtering and Signal Processing. St. Paul, MN: West Publishing, 1975.
66. J. L. Flanagan, Speech Analysis, Synthesis, and Perception, 2nd Ed. New York: Springer-Verlag, 1972.
67. B. S. Atal “Effectiveness of linear prediction characteristics of the speech wave for automatic speaker identification and verification,” J. Acoust. Soc. Amer, vol. 55, pp. 1304–1312, June 1974.
68. D. G. Childers, R. S. Varga, and N. W. Perry, Jr. “Composite signal decomposition,” IEEE Trans. Audio Electroacoust, vol. AU-18, pp. 471–477, Dec. 1970.
69. M. P. Ekstcom “A spectral characterization of the ill-conditioning in numerical deconvolution,” IEEE Trans. Audio Electroacoust. vol. AU-21, pp. 344–348, Aug. 1973.
70. B. R. Hunt “A theorem on the difficulty of numerical deconvolution,” IEEE Trans. Audio Electroacoust., vol. AU-20, pp. 94–95, Mar. 1972.
71. — “Deconvolution of linear systems by constrained regression and its relationship to the Wiener theory,” IEEE Trans. Automat. Contr., vol. AC-17, pp. 703–705, Oct. 1972.
72. J. Makhoul, “Linear prediction: a tutorial review,” Proc. IEEE, vol. 63, pp. 561–580, Apr. 1975.
73. B. Mitchell, M. Landisman, and Z. A. Der “Predictive deconvolution applied to long range seismic refraction observations,” Pure Appl. Geophysics, vol. 96, pp. 127–133, 1972.
74. K. L. Peacock and S. Treitel “Predictive deconvolution: theory and practice,” Geophysics, vol. 34, pp. 155–169, Apr. 1969.
75. E. A. Robinson “Predictive decomposition of seismic traces,” Geophysics, vol. 22, pp. 767–778, 1957.
76. — “Properties of the Wold decomposition of stationary stochastic processes,” Theory Prob. Appl., vol. 8, pp. 187–194, 1963.
77. — “Mathematical development of discrete filters for the detection of nuclear explosions,” J. Geophysics Res., vol. 68, pp. 5559–5567, 1963.
78. — “Multichannel z-transforms and minimum delay,” Geophysics, vol. 31, pp. 482–500, June 1966.
79. — “Predictive decomposition of time series with application to seismic exploration,” Geophysics, vol. 32, pp. 418–484, June 1967.
80. J. Schell, “Dereverberation by linear systems techniques,” IEEE Trans. Geosci. Electron., vol. GE-9, no. 1, pp. 28–34, Jan. 1971.
81. L. C. Wood and S. Treitel “Seismic signal processing,” Proc. IEEE, vol. 63, pp. 649–661, Apr. 1975.
82. M. Bath, Mathematical Aspects of Seismology. Amsterdam: Elsevier, 1968.
83. Computational Seismology, V. I. Keilis-Borok, Ed. New York: Consultants Bureau, 1972.
84. E. A. Robinson, Multichannel Time Series Analysis with Digital Computer Programs. San Francisco: Holden-Day, 1967.
85. —, Statistical Communication and Detection with Special Reference to Digital Data Processing of Radar and Seismic Signals. New York: Hafner, 1967.
86. E. A. Robinson and S. Treitel, Robinson-Treitel Reader, 3rd Ed. Tulsa, OK: Seismographic Service Corp., 1973.
87. Seismic Filtering, R. Van Nostrand, Ed. Tulsa, OK: Society of Exploration Geophysicists, 1971.