Signals and Signal Processing

  • Eugen Skudrzyk


It is very important that methods be developed to extract signals from the noisy backgrounds that usually accompany them. Signal processing has, therefore, become an important field in communications and in acoustics. The human ear processes the information it receives and does a reasonably good job of filtering. A knowledge of the signal processing techniques that have been developed in the past will also be helpful in understanding the functioning of the human ear.


False Alarm Wave Form Noise Power Delay Line Matched Filter 


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  1. Anderson, V. C.: DELTIC correlator. Harvard Acoust. Lab. Tech. Memo. No. 37, Jan. 5, 1956.Google Scholar
  2. Bartberger, C. L., Russo, D. M.: Ambiguity diagram for linear FM sonar. J.A.S.A. 38 (1965) 183.Google Scholar
  3. Beer, F. P., Rice, J. R.: First-occurrence time of high-level crossings in a continuous random process. J.A.S.A. 39 (1966) 323.MATHMathSciNetGoogle Scholar
  4. Bennett, W. R.: Response of a linear rectifier to signal and noise. J.A.S.A. 15 (3) (1944) 165–172;Google Scholar
  5. Bennett, W. R.: Methods of solving noise problems. I.R. E. Proc. 44 (1956) 609–638.Google Scholar
  6. Bennett, W. R., Rice, S. O.: Note on methods of computing modulation products. Philosophical Magazine, series 7, 18 (1934) 422–424.Google Scholar
  7. Bernfeld, M., Cook, C. E., Paolillo, J., Palmieri, C. A.: Matched filtering, pulse compression and waveform design. Microwave Journal, Oct., Nov., Dec., 1964; Jan., 1965.Google Scholar
  8. Birdsall, T. G., Roberts, R. A.: Theory of signal detectability: deferred-decision theory. J.A.S.A. 37 (1965) 1064.Google Scholar
  9. Blackman, R. B., Tukey, J. W.: The measurement of power spectra from the point of view of communications engineering. Bell Sys. Tech. J. 37 (1958) 185–282, 485–569.MathSciNetGoogle Scholar
  10. Blasbalg, H.: The sequential detection of a sine-wave carrier of arbitrary duty ratio in Gaussian noise. I.R. E. Trans. IT-3 (1957) 248–256.Google Scholar
  11. Bode, H. W., Shannon, C.: A simplified derivation of linear least-square smoothing and prediction theory. I.R. E. Proc. 38 (1950) 417–425.MathSciNetGoogle Scholar
  12. Booton, R. C.: An optimization theory for time-varying linear systems with non-stationary statistical inputs. I.R. E. Proc. 40 (1952) 977–981.Google Scholar
  13. Bryn, F.: Optimum signal processing of three-dimensional arrays operating on Gaussian signals and noise. J.A.S.A. 34 (1962) 289.MathSciNetGoogle Scholar
  14. Bunimovich, V. I.: Fluctuation processes in radio receivers. Sovietskoe Radio, 1951 (in Russian).Google Scholar
  15. Burgess, R. E.: The rectification and observation of signals in the presence of noise. Philosophical Magazine, series 7, 42 (328) (1951) 475–503.MATHGoogle Scholar
  16. Callen, H. B., Welton, Tr. A.: Irreversibility and generalized noise. Phys. Rev. 83 (1): 34 40, July 1, 1951.Google Scholar
  17. Carnap, R.: Logical foundations of probability. Chicago: University of Chicago Press. 1950.MATHGoogle Scholar
  18. Corn, F. W.: Introduction to sonar technology. Tracor, Inc., Bureau of Ships — Navy Department — Washington, D.C., December 1965.Google Scholar
  19. Cutrona, L. J., Leith, E. N., Palermo, C. J, Porcello, L. J.: Optical data processing and filtering systems. I.R.E. Trans. IT-6 (1960) 386–400.Google Scholar
  20. Davenport, W. B., JR., ROOT, W. L.: An introduction to the theory of random signals and noise. New York, N. Y.: McGraw-Hill 1958.Google Scholar
  21. Dwork, B. M.: The detection of a pulse superposed on fluctuation noise. I.R. E. Proc. 38 (1950) 771–774.MathSciNetGoogle Scholar
  22. Emerson, R. C.: First probability densities for receivers with square-law detectors. J. Appl. Phys. 24 (9) (1953) 1168–1176.ADSCrossRefGoogle Scholar
  23. Enochson, L. D., Goodman, N. R.: Gaussian approximation to the distribution of sample coherence. AFFDL TR 65 57, Research and Technology Division, AFSC, Wright-Patterson AFB, Ohio, February 1965.Google Scholar
  24. Faxley, D. C.: Comparison between the performances of a time averaged product array and an intraclass correlator. J.A.S.A. 31 (1959) 1307.Google Scholar
  25. Fano, R. M.: Signal-to-noise ratios in correlation detectors. MIT Research Lab. Electronics Tech. Rept. 186, Feb. 19, 1951.Google Scholar
  26. Fleischmann, B. S.: The optimum log Io detector for the detection of a weak signal in noise. Radiotekh. i Elektron. 2 (1957) 726–734.Google Scholar
  27. Fowle, E. N.: A method of designing FM pulse compression signals. I.R. E. Trans. IT-10 (1964) 61–67.Google Scholar
  28. Galejs, J.: Enhancement of pulse train signals by comb filters. I.R. E. Trans. IT-4 (1958) 114–125.Google Scholar
  29. George, S. F.: Effectiveness of crosscorrelation detectors. Proc. Natl. Electronics Conf. (Chicago) 10 (1954) 109–118.Google Scholar
  30. George, S. F., Zamanakos, A. S.: Comb filters for pulsed radar use. I.R. E. Proc. 42 (1954) 1159–1165.Google Scholar
  31. Green, P. E., Jr.: The output signal-to-noise ratio of correlation detectors. I.R.E. Trans. IT-3, 1 (1957) 10–18.Google Scholar
  32. Harmon, W.: Principles of the statistical theory of communication. New York, N. Y.: McGraw-Hill. 1963.Google Scholar
  33. Harrington, J. V.: An analysis of the detection of repeated signals in noise by binary integration. I.R. E. Trans. IT-1 (1955) 1–9;Google Scholar
  34. Harrington, J. V.: Signal-to-noise improvement through integration in a storage tube. I.R. E. Proc. 38 (1950) 1197–1203.Google Scholar
  35. Helstrom, C. W.: Statistical theory of signal detection. Braunschweig: Pergamon Press, Inc. 1968.Google Scholar
  36. Huggins, W. H.: A phase principle for complex-frequency analysis and its implications in auditory theory. J.A.S.A. 24 (1952) 582–586.Google Scholar
  37. Jenkins, W. H., Brouneus, H. A.: Photoelastic ultrasonic delay:lines. Proc. Natl. Electron. Conf. 16 (1960) 835–839.Google Scholar
  38. Jury, E. I.: Theory and application of the Z-transform method. New York, N. Y.: Wiley. 1964.Google Scholar
  39. Kac, M., Siegert, A. J. F.: On the theory of noise in radio receivers with square law detectors. J. Appl. Phys. 18 (1947) 383–397.ADSCrossRefMathSciNetGoogle Scholar
  40. Kailath, T.: A projection method for signal detection in colored Gaussian noise. I. E.E.E. Trans. IT-13 (1967) 441–447.Google Scholar
  41. Kelly, E. J., Reed, I. S., Root, W. L.: The detection of radar echoes in noise. J. Soc. Ind. Appl. Math. 8, (I) 309–341, (II) 481–507, 1960.MathSciNetGoogle Scholar
  42. Klauder, J. R., Price, A. C., Darlington, S., Albersheim, W. J.: The theory and design of chirp radars. Bell System Techn. J. 39 (1960) 745–808.Google Scholar
  43. Korn: A physical theory of the transmission of information. Soy. Phys. Acoust. 22 (1969–70) 267–274.Google Scholar
  44. Landau, H. J., Pollak, H. O.: Prolate spheroidal wave functions, Fourier analysis and uncertainty, II. Bell Sys. Tech. J. 40 (1961) 65–84;MATHMathSciNetGoogle Scholar
  45. Landau, H. J., Pollak, H. O.: Prolate spheroidal wave functions, Fourier analysis and uncertainty, III. Bell Sys. Tech. J. 41 (1962)1295–1336.Google Scholar
  46. Laning, J. H., Jr., Battin, R.H.: Random processes in automatic control. New York, N. Y.: McGraw-Hill. 1956.Google Scholar
  47. Lawson, J. L., Uhlenbeck, G. E. (Eds.): Threshold signals. MIT radiation laboratory series, Vol. 24, Sec. 7. 5. New York, N. Y.: McGraw-Hill 1950.Google Scholar
  48. Lee, Y. W.: Statistical theory of communication. New York, N. Y.: Wiley. 1964.Google Scholar
  49. Lee, Y. W., Cheatram, T. P., JR., Wiesner, J. B.: Application of correlation analysis to the detection of periodic signals in noise. I.R.E. Proc. 38 (1950) 1165–1171.Google Scholar
  50. Lee, Y. W., Wiesner, J. B.: Correlation functions and communication applications.Electronics 23 (1950) 86–92.Google Scholar
  51. Lerner, R. M.: A matched filter detection system for complicated Doppler shifted signals. I.R. E. Trans. IT-6 (1960) 373–385.Google Scholar
  52. Levinson, N.: A heuristic exposition of Wiener’s mathematical theory of prediction and filtering. J. Math. Phys. 26 (1947) 110–119. Also appendix C of Wiener (III).Google Scholar
  53. Licklider, J. C. R.: Basic correlates of the auditory stimulus, in S. S. STEVENS (Ed.),Handbook of experimental psychology, p. 1009. New York, N. Y.: Wiley. 1951.Google Scholar
  54. Lynch, W. A., Truxal, J. G.: Signals and systems in electrical engineering, Part 1,Part 2. New York, N. Y.: McGraw-Hill. 1962.Google Scholar
  55. Martel, H. C., Mathews, M. V.: Further results on the detectability of known signals in Gaussian noise. Bell Sys. Tech. J. 40 (1953) 423–451MathSciNetGoogle Scholar
  56. Mcfadden, D.: Lateralization and detection of a tonal signal in noise. J.A.S.A. 45 (1969) 1505.Google Scholar
  57. Meyer, M. A., Middleton, D.: On the distributions of signals and noise after rectification and filtering. J. Appl. Physics 25 (8) (1954) 1037–1052.ADSMATHCrossRefMathSciNetGoogle Scholar
  58. Middleton, D.: The response of biased, saturated linear, and quadratic rectifiers to random noise. J. Appl. Physics 17 (1946) 778 801;ADSCrossRefMathSciNetGoogle Scholar
  59. Middleton, D.: Some general results in the theory of noise through nonlinear devices. Quart. Applied Math. 5 (4) (1948) 445–498;MATHMathSciNetGoogle Scholar
  60. Middleton, D.: The distribution of energy in randomly modulated waves. Philosophical Magazine, series 7, 42 (1951) 689–707;MathSciNetGoogle Scholar
  61. Middleton, D.: Statistical methods for the detection of pulsed radar in noise, in W. Jackson(Ed.), Communication theory, pp. 241–270, Academic Press, New York, and Butterworth’s Scientific Publications, London, 1953;Google Scholar
  62. Middleton, D.: Statistical criteria for the detection of pulsed carriers in noise, Parts I and II. J. Appl. Physics 24 (1953) 371–391;ADSMATHCrossRefMathSciNetGoogle Scholar
  63. Middleton, D.: also letters to the editor by D. Middletonet al. in J. Appl. Physics, January, 1954Google Scholar
  64. Middleton, D.: An introduction to statistical communication theory. New York, N. Y.: McGraw-Hill 1960;Google Scholar
  65. Middleton, D.: On new classes of matched filters and generalizations of the matched filter concept. I.R. E. Trans. IT-6 (1960) 349–360.Google Scholar
  66. Middleton, D., Meter, D. Van: Detection and extraction of signals in noise from the viewpoint of statistical decision theory. J. Soc. Ind. Appl. Math. 3 (1955) 192–253, and 4 (1956) 86–119.CrossRefGoogle Scholar
  67. North, D. O.: An analysis of the factors which determine signal-noise discrimination in pulsed carrier systems. RCA Laboratory Report PTR-6C; reprinted in I. E.E.E. Proc. 51 (1963) 1016–1027.Google Scholar
  68. O’meara, T. R.: The synthesis of band-pass all-pass time delay networks with graphical approximation techniques. Hughes Res. Rept. No. 114, 1959.Google Scholar
  69. Parzen, E.: Extraction and detection problems and reproducing Kernel Hilbert spaces. J. Soc. Ind. Appl. Math., Series A on control, 1 (1962) 35–62.MATHCrossRefMathSciNetGoogle Scholar
  70. Peterson, W. W., Birdsall, T. G., Fox, W. C.: The theory of signal detectability.I.R. E. Trans. PGIT-4 (1953) 171–212.Google Scholar
  71. Pick, G. C., Gray, S. B., Brick, D. B.: The solenoid array—a new computer element. I. E.E.E. Trans. Electron Computers 13 (1964) 27 35.Google Scholar
  72. Price, R.: The detection of signals perturbed by scatter and noise. I.R. E. Trans. PGIT-4 (1954) 163–170;Google Scholar
  73. Price, R.:A note on the envelope and phase-modulated components of narrow-band Gaussian noise. I.R. E. Trans. IT-1 (2) (1955) 9–13;Google Scholar
  74. Price, R.:Optimum detection of random signals in noise with application to scatter multipath communications I., I.R.E. Trans. IT-2 (4): December, 1956.Google Scholar
  75. Reich, E., Swerling, P.: The detection of a sine wave in Gaussian noise. J. Appl. Physics 24 (3) (1953) 289–296.ADSMATHCrossRefMathSciNetGoogle Scholar
  76. Remley, W. R.: Some effects of clipping in array processing. J.A.S.A. 391 (1966) 702.Google Scholar
  77. Root, W. L.: Singular Gaussian measures in detection theory. ROSENBLATT, M. (Ed.),Proc. Symp. on Time Series Analysis. New York, N. Y.: Wiley. 1963, 292–315.Google Scholar
  78. Root, W. L., Pitcher, T. S.: On the Fourier-series expansion of random functions.Annals of Math. Statistics 26 (2) (1955) 313–318;MATHCrossRefMathSciNetGoogle Scholar
  79. Root, W. L., Some remarks on statistical detection. I.R. E. Trans. IT-1 (3) (1955) 33–38.Google Scholar
  80. Rowlands, R. O.: Detection of a Doppler-invariant FM signal by means of a tapped delay line. J.A.S.A. 37 (1965) 608–615;Google Scholar
  81. Rowlands, R. O.:Matched filter and correlation techniques, in Underwater Acoustics by V. M. Albers, Vol. 2. Plenum Press, 1967;Google Scholar
  82. Rowlands, R. O.:The relative efficiencies of various binary detection systems. I.R.E. Intern. Cony. Record, 1962;Google Scholar
  83. Rowlands, R. O.:FM signals tailored to specific sonar and radar requirements. Paper 7.4, Wescon (West Coast Convention), I.E.E.E., 1963.Google Scholar
  84. Rudnick, P.: Likelihood detection of small signals in stationary noise. J. Appl. Physics 32 (1961) 140–143.ADSCrossRefMathSciNetGoogle Scholar
  85. Selin, I.: Detection theory. Princeton, N. J.: Princeton University Press. 1955.Google Scholar
  86. Shannon, C.: A mathematical theory of communication. Bell Sys. Tech. J. 27 (1948)379–423, 623–655;Google Scholar
  87. Shannon, C.:Communication in the presence of noise. I.R. E. Proc. 37 (1949) 10–21.MathSciNetGoogle Scholar
  88. Spooner, R. L.: On the detection of a known signal in a non-Gaussian noise process. J.A.S.A. 44 (1968) 141.Google Scholar
  89. Stumpers, F. L.: A bibliography of information theory (communication theory—cybernetics). I.R.E. Trans. PGIT-2, November, 1953;Google Scholar
  90. Stumpers, F. L.: Supplement to a bibliography of information theory (communication theory—cybernetics). I.R. E. Trans. IT-1 (2) (1955) 31–47.Google Scholar
  91. Sussman, S. M.: A matched filter communication system for multipath channels. I.R. E. Trans. IT-6 (1960) 367 373.MathSciNetGoogle Scholar
  92. Thor, C.: A large time-bandwidth product technique. I.R.E. Trans. Mil. Electron. 6 (1962) 169–173.CrossRefGoogle Scholar
  93. Titsworth, R. C.: Coherent detection by quasi-orthogonal square-wave pulse functions. I.R. E. Trans. IT-6 (1960) 410–411.Google Scholar
  94. Turin, G. L.: I. Communication through noisy random-multipath channels. I.R.E. Convention Record, Part 4 (1956) 154–166;Google Scholar
  95. Turin, G. L.:Error probabilities for binary symmetric ideal reception through non-selective slow fading and noise. I.R. E. Proc. 46 (1958) 1603 1619;Google Scholar
  96. Turin, G. L.:On the estimation in the presence of noise of the impulse response of a random, linear filter. I.R. E. Trans. IT-3 (1957) 5–10;Google Scholar
  97. Turin, G. L.:An introduction to matched filters. I.R. E. Trans. IT-6 (1960) 311–329.Google Scholar
  98. Vleck, J. H. Van, Middleton, D.: A theoretical comparison of visual, aural, and meter reception of pulsed signals in the presence of noise. J. Appl. Physics 17 (1946) 940–971.Google Scholar
  99. Westerfield, E. C., Prager, R. H., Stewart, J. L.: Processing gains against reverberation (clutter) using matched filters. I.R. E. Trans. IT-6 (1960) 342–348.Google Scholar
  100. Winder, A. A., Loda, CH. J.: Introduction to acoustical space-time information processing ONR Report ACR063 (January 1963).Google Scholar
  101. Woodward, P. M., Davies, I. L.: Information theory and inverse probability in telecommunication. I. E.E. Proc. 99 (1952) 37–44.MathSciNetGoogle Scholar
  102. Zadeh, L. A.: Optimum non-linear filters. J. Appl. Physics 24 (1953) 396–404.ADSMATHCrossRefMathSciNetGoogle Scholar
  103. Zadeh, L. A., Ragazzini, J. R.: Optimum filters for the detection of signals in noise. I.R. E. Proc. 40 (1952) 1223–1231.Google Scholar

Copyright information

© Springer-Verlag/Wien 1971

Authors and Affiliations

  • Eugen Skudrzyk
    • 1
  1. 1.Ordnance Research Laboratory and Physics DepartmentThe Pennsylvania State UniversityUniversity ParkUSA

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