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Abstract

It was recognized very early during the development of communications that the possible transmission rate of symbols of a communication channel depended on its frequency respon.se of attenuation and phase shift. For instance, the famous theorem by NYQUIST [1] and KÜPFMÜLLER [2, 3] st ate s that one independent symbol may be transmitted per time interval of duration τ through an idealized frequency lowpass filter of bandwidth Δf, where

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References ordered by Sections

  1. DOOB, J.L., Stochastic processes, New York: Wiley1953.

    Google Scholar 

  2. VAN DER ZIEL, A., Noise, Englewood Cliffs NJ: Prentice Hall 1954.

    Google Scholar 

  3. RICE, S.O., Mathematical analysis of random noise, Bell System Tech. J. 23(1944),282–332, 24 (1945), 46–156.

    MathSciNet  MATH  Google Scholar 

  4. SMUIJLIN, D. and H.A.HAUS, Noise in electron devices, New York: Wiley 1959.

    Google Scholar 

  5. BENNETT, W.R., Electrical noise, New York: McGraw-Hill 1960.

    Google Scholar 

  6. DAVENPORT, W.B.jr. and W.L.ROOT, An introduction to the theory of random signals and noise, New York: McGraw-Hill 1958.

    MATH  Google Scholar 

  7. SCHWARTZ, M., Information transmission, modulation, and noise, New York: McGraw-Hill 1959.

    MATH  Google Scholar 

  8. ROOT, W.L. and T.S.PITCHER, On the Fourier-series expansion of random functions, Annals of Math.Statistics 26 (1955), 313–318.

    Article  MathSciNet  MATH  Google Scholar 

  9. HAUS, H.A., a.o. IRE standards of methods of measuring noise in linear twoports, Proc.IRE 48(1960),60–68.

    Article  Google Scholar 

  10. DÖRR, K., Die statistische Verteilung der Nulldurchgänge von Rauschspannungen, Archiv elek. Übertragung 19 (1965), 685–698.

    Google Scholar 

  11. SZALAY, G., Die Verteilungsdichte der Intervalle bei einem Rauschsignal mit Schwellwert, Archiv elek.Übertragung 18 (1964), 316–322.

    Google Scholar 

  12. JOHNSON, J.B., Thermal agitationof electricityin. con-ductors, Physical Review 32 (1928), 97–109.

    Article  Google Scholar 

  13. KOTEL’NIKOV, V.A., The theoryof optimum noise immuni-ty (translation of the Russian original published in1947, by R.A.SILVERMAN), New York: McGraw-Hill 1959.

    Google Scholar 

  14. SIEBERT, W.M. and W.L.ROOT, Statistical decision theo-ry and communications, in Lectures on communication sy-stem theory, New York: McGraw-Hill 1961.

    Google Scholar 

  15. MIDDLETON, D., An introductionto statistical communi-cation theory; New York: McGraw-Hill 1960.

    Google Scholar 

  16. WAINSTAIN, L.A. and V.D.ZUBAKOV, Extractionof sign.als from noise, Englewood Cliffs NJ: Prentice Hall 1962.

    Google Scholar 

  17. HARMAN, W.A., Principles of the statistical theory of communj:cation; New York: McGraw-Hill 1963.

    Google Scholar 

  18. WIENER, N., Extrapolation, interpolation and smoothing of stationary time series, New York: MIT Press and Wiley 1949.

    MATH  Google Scholar 

  19. HANCOCK, J.C., Signal detection theory, New York: McGraw-Hill 1966.

    Google Scholar 

  20. LEVINSON, N., The Wiener RMS error criterioninfilter design and prediction, J. of Math. and Physics 25 (1947), 261–278.

    MathSciNet  Google Scholar 

  21. KOLMOGOROFF,.A., Interpolation and extrapolation of stationary random sequencies, Bulletin de l’académie des sciences de USSR, Ser.Math. 5 (1941), 3–14.

    Google Scholar 

  22. SHERMAN, S., Non-mean square error criteria IRE Trans-actions on Information Theory IT-4(1959)0252126.

    Google Scholar 

  23. BODE, H.W. A simplified derivation of linear least-square smoothing and prediction theory, Proc. IRE 38 (1950), 417–426.

    Article  MathSciNet  Google Scholar 

  24. ARTHURS, E. and H.DYM, On.the optimum detection of di-gital signals in the presence of white Gaussian noise, IRE Transactions on Communication Systems CS-10(1962), 336–372.

    Article  Google Scholar 

  25. NORTH, D.O., An analysis of the factors which determine signal/noise discrimination in. pulsed-carrier systems, re-printed in Proc. IEEE 51(1963)0016–1027.

    Google Scholar 

  26. TURIN, G.L., An introduction to matched filters, IRE Transactions on Information Theory IT-6(1960),311–329.

    Article  MathSciNet  Google Scholar 

  27. SCHUSSLER, W., tiler den Entwurf optimaler Suchfilter, NTZ 17 (1964), 605–613.

    Google Scholar 

  28. SCHLITT, H., SystemtheoriefiirregelloseVorgänge, Ber-lin/New York: Springer 1960.

    Google Scholar 

  29. ZADEH, L.A. and I.R.RAGAZZINI, Optimum filters forthe detection.of signals innoise, Proc.IRE 40(1952)0123–1131.

    Google Scholar 

  30. PETERSON, E.L., Statistical analysis and optimization of systems, New York: Wiley 1961.

    MATH  Google Scholar 

  31. CORRINGTON, M.S. and R.N.ADAMS, Advanced analytical and signal processing techniques: Application of Walshfunctions to nonlinear analysis, Technical Report AD-277942(1962).

    Google Scholar 

  32. WEISER, F.E., Walsh function analysis of instantaneous nonlinear stochastic problems, Thesis, Polytechnic Institute of Brooklyn (1964).

    Google Scholar 

  33. BAGHDADY, E.J., Diversity techniques, in Lectures on communication system theory; New York: McGraw-Hill 1961.

    Google Scholar 

  34. BRENNAN, D.G., Linear diversity combining techniques, Proc. IRE 47 (1959), 1075–1102.

    Article  Google Scholar 

  35. PIERCE, J.N. and S.STEIN, Multiple diversity with non-independent fading, Proc. IRE 48 (1960), 89–104.

    Article  Google Scholar 

  36. PRICE, R., Optimum detection of random signals in noise with application to scatter multipath communications, IRE Transactions on Information Theory IT-2(1956),125–135.

    Google Scholar 

  37. PRICE, R. and P.E. GREEN, A communication technique for multipath channels, Proc.IRE 46 (1958), 555–570.

    Article  Google Scholar 

  38. GLEN, A.B., Comparison of PSK vs FSK and PSK-AM vs FSK-AM binary coded transmission systems, IEEE Transactions on Communication Systems CS-8(1960),87–100.

    Google Scholar 

  39. RIDOUT, P.N. and L.K.WHEELER, Choice of multi-channel telegraph systems for useon HF radio links, Proc.IEE 110 (1963), 1402–1410.

    Google Scholar 

  40. TURIN, G.L., On optimal diversity reception I, IRE Transactions on Information Theory IT-7(1961),154–166.

    Google Scholar 

  41. On optimal diversity reception II, IRE Transactions on Communication Systems CS-10(1962),22–31.

    Google Scholar 

  42. LAW, H.B., The detectability of fading radiotelegraph signals in noise, Proc.IEE 104B(1957),130–140.

    Google Scholar 

  43. VOELCKER, H.B., Phase shift keying in fading channels, Proc.IRE 107B (1960), 31–38.

    Google Scholar 

  44. PIERCE, J.N., Theoretical diversity improvement in frequency-shift keying, Proc.IRE 46(1958),903-910.

    Google Scholar 

  45. ALNATT, J.W., E.D.JONES and H.B.LAW, Frequency diversity in the reception of selective fading binary frequency -modulated signals, Proc.IEE 104B(1957),98–11.0.

    Google Scholar 

  46. BELLO, P.A. and B.D.NELIN, The effect of frequency selective fading on the binary error probabilities of incoherent and differentially coherent matched filter receivers, IEEE Transactions on Communication Systems CS-11 (1963), 170–186.

    Google Scholar 

  47. BESSLICH, Ph., Fehlerwahrscheinlichkeit binärer Übertragungsverfahren bei Störure en durch Rauschen und Schwund, Archiv elek. Übertragung 17 (1963), 185–197.

    Google Scholar 

  48. Fehlerwahrscheinlichkeit binärer Übertragungen bei Mehrfachempfang und frequenz-selektivem Schwund, Archiv elek. Übertragung 17 (1963), 271–277.

    Google Scholar 

  49. ZUHRT, H., Die Summenhäufigkeitskurven der exzentrischen Rayleigh-Verteilung und ihre Anwendung auf Ausbreitungsmessungen, Archiv elek.Übertragung 11(1957),478–484.

    Google Scholar 

  50. HENZE, E., Theoretische Untersuchungen über einige Diversity-Verfahren, Archiv elek. Übertragung 11 (1957), 183–194.

    MathSciNet  Google Scholar 

  51. SCHWARTZ, M., W.R.BENNETT and S.STEIN, Communication systems and techniques, New York: McGraw-Hill 1966.

    Google Scholar 

  52. GROSSKOPF, J., M.SCHOLZ and K.VOGT, Korrelationsmes-sungen im Kurzwellenbereich, NTZ 11 (1958), 91–95.

    Google Scholar 

  53. NYQUIST, H., Certain topics in telegraph transmission theory, Transactions AIEE 47 (1928), 617–644.

    Google Scholar 

  54. KUPFMULLER, K., ‘Ober Einschwingvorgänge in Wellenfil-tern, Elektrische Nachrichten-Technik 1(1924)041–152.

    Google Scholar 

  55. Ausgleichsvorgänge und Frequenzcharakteristiken in linearen Systemen, Elektrische Nachrichten-Technik 5 (1928), 18–32.

    Google Scholar 

  56. HARTLEY, R.V.L., Transmissionof information, Bell Sy-stem Tech.J. 7 (1928), 535–563.

    Google Scholar 

  57. KUPFKILLER, K., Die Systemtheorie der elektrischen Nachrichtenübertragung, Stuttgart: Hirzel 1952.

    Google Scholar 

  58. SHANNON, C.E., A mathematical theoryof communication, Bell System Tech.J. 27(1948),379–423, 623–656.

    Google Scholar 

  59. Communication in the presence of noise, Proc. IRE 37 (1949), 10–21.

    Google Scholar 

  60. FANO, R.M., Transmission of information, New York: MIT Press and Wiley 1961.

    Google Scholar 

  61. SCHMIDT, K.O., Vorschläge zur Berechnung der wirkli-chen Kanalkapazität beim Vorhandensein vonVerlusten auf dem tbertragungswege, Archiv elek. Ubertragung 8 (1954), 19–26.

    Google Scholar 

  62. ZEMANEK, H., Elementare Informationstheorie,Wien: 01- denburg 1959.

    Google Scholar 

  63. FEY, P., Informationstheorie, Berlin: Akademie 1963.

    MATH  Google Scholar 

  64. SOMMERVILLE, D.M.Y., An introduction to the geometry of N dimensions, New York: Dutton 1929.

    MATH  Google Scholar 

  65. MADELUNG, E., Die mathematischen Hilfsmittel des Phy-sikers, Berlin/New York: Springer 1957.

    Google Scholar 

  66. HARMUTH, H., Die ttbertragungskapazität von Nachrich-tenkanälen nach der Verallgemeinerung des Begriffes Fre-quenz, Archiv elek. tlbertragung 19(1965)025–133.

    Google Scholar 

  67. SOMMERFELD, A., Uber die Fortpflanzung des Lichtes in dispergierenden Medien, Ann.Phys. 44 (1914), 177–202.

    Article  Google Scholar 

  68. DAVENPORT, W.B.Jr. and W.L.ROOT, An introduction to the theoryof random signals and noise, New York: McGraw-Hill 1958.

    Google Scholar 

  69. HARMAN, W.W., Principles of the statistical theory of communication, New Yorkt McGraw-Hill 1963.

    Google Scholar 

  70. WAINSTEIN, L.A. and V.D. ZUBAKOV, Extraction of sig-nalsfromnoise, Englewood Cliffs NJ: Prentice Hall 1962.

    Google Scholar 

  71. HARMUTH, H., P.E.SCHMID and H.S.DUDLEY, Multiple ac- cess communication with binary orthogonal sine and cosine pulses using heavy amplitude clipping, 1968 IEEE Int. Conf.on Communications Record pp. 794–799.

    Google Scholar 

  72. VAN VLECK, J.H., and D.MIDDLETON, The spectrum of clip-ped noise, Proc.IEEE 54 (1966), 2–19.

    Article  Google Scholar 

  73. SUNDE, E.D., Ideal binarypulse transmission. by AM and FM, Bell System Tech.J. 38(1959),1357–1426.

    Google Scholar 

  74. AIKENS, A.J. and D.A.LEWINSKI, Evaluation of message circuit noise, Bell System Tech.J. 39 (1960), 879–909.

    Google Scholar 

  75. SMITH, D.B. and W.E.BRADLEY, The theory of impulse noise in ideal frequency-modulation receivers, Proc. IRE

    Google Scholar 

  76. ),743–751.

    Google Scholar 

  77. BENNETT, W.R., Electrical noise, New York: McGraw-Hill 1960.

    Google Scholar 

  78. STUMPERS, F.L., On the calculation of impulse-noise transients infrequency-modulation receivers, Philips Re-search Repts. 2 (1947), 468–474.

    MathSciNet  Google Scholar 

  79. HARMUTH, H., Kodierenmitorthogonalen Funktionen, Ar-chiv elek. Ubertragung 17(1963),429–437,508–518.

    Google Scholar 

  80. HAMMING, R.W., Error detecting and error correcting codes, Bell System Tech.J. 29 (1950), 147–160.

    MathSciNet  Google Scholar 

  81. SLEPIAN, D., A class of binary signaling alphabets, Bell System Tech.J. 35 (1956), 203–234.

    MathSciNet  Google Scholar 

  82. WOZENCRAFT, J.M. and B.REIFFEN, Sequential decoding, New York: MIT Press and Wiley 1961.

    MATH  Google Scholar 

  83. GALLAGER, R.G., Low-density parity-check codes, Cam-bridge, Mass.: MIT-Press 1963.

    Google Scholar 

  84. MULLER, D.E., Applicationof Boolean algebrato switch-ing circuit design and to error detection, IRE Transactions on Electronic Computers EC-3(1954),6–12.

    Google Scholar 

  85. PETERSON, W.W., Error correcting codes, New York: MIT Press and Wiley 1961.

    MATH  Google Scholar 

  86. Progress of information theory 1960–63, IEEE Trans-actions on Information Theory IT-10(1963),21–264.

    Google Scholar 

  87. LEE, C.Y., Some properties of non-binary error correc-ting codes, IRE Transactions on Information Theory IT-4

    Google Scholar 

  88. -82.

    Google Scholar 

  89. ULRICH, W. Non-binary error correcting codes, Bell System Tech.J. 36 (1957), 1341–1388.

    Google Scholar 

  90. REED, I.S., A class of multiple-error-correcting codes and the decoding scheme, IRE Transactions on Information Theory IT-4(1954),38–49.

    Google Scholar 

  91. WEISS, P., Uber die Verwendung von Walshfunktionen in der Codierungstheorie, Archivelek. Ubertragung 21 (1967), 255–258.

    Google Scholar 

  92. GOLOMB, S.W., L.D.BAUMERT, M.F.EASTERLING, J.J.STIFF-LER and A. J.VITERBI, Digital communications, Englewood Cliffs NJ: Prentice Hall 1964.

    Google Scholar 

  93. HARMUTH, H., Orthogonal codes, Proc. IEE 107C (1960), 242–248.

    MathSciNet  Google Scholar 

  94. ARONSTEIN, R.H., Comparison of orthogonal and block codes, Proc. IEE 110 (1963), 1965–1967.

    Google Scholar 

  95. HSIEH, P. and M.Y.HSIAO, Several classes of codes generated from orthogonal functions, IEEE Transactions on Information Theory IT-10(1964),88–91.

    Google Scholar 

  96. FANO, R. Communication in the presence of additive Gaussian noise, in Communication Theory, New York: Academic Press 1953.

    Google Scholar 

  97. LACHS, G., Optimization of signal waveforms, IEEE Trans-actions on Information Theory IT-9(1963),95–97.

    Google Scholar 

  98. PALEY, R.E., On orthogonal matrices, J.Math. and Physics 12 (1933), 311–320.

    Google Scholar 

  99. STANTON, R.G. and D.A. SPROTT, A family of difference sets, Canadian J.of Math. 10 (1958), 73–77.

    Article  MathSciNet  MATH  Google Scholar 

  100. BOSE, R.C. and S.S.SHRIKANDE, A note on a result in the theory of code construction, Information and Control 2(1959)083–194.

    Google Scholar 

  101. NEIDHARDT, P. Informationstheorie und automatische Informationsverarbeitung, Berlin: Verlag Technik 1964.

    Google Scholar 

  102. WOOD, H., Random normal deviates, Tracts for Computers 25, London: Cambridge University Press 1948.

    Google Scholar 

  103. US Department of Commerce, Handbook of mathematical functions, National Bureau of Standards Applied Mathematical Series 55, Washington DC: US Government Printing Office 1964.

    Google Scholar 

  104. The RAND Corporation, A million random digits with 100 000 normal deviates, Glencoe Ill.: The Free Press1955.

    Google Scholar 

  105. PETERSON, W.W., Error correcting codes, New York: MIT Press and Wiley 1961.

    MATH  Google Scholar 

  106. ETIAS, P., Error-free coding, IRE Transactions on Information Theory IT-4(1954),29–37.

    Google Scholar 

  107. HARMUTH, H., Kodieren mit orthogonalen Functionen, II. Kombinations-Alphabete und Minimum-Energie-Alphabete, Archiv elek. tibertragung 17 (1963), 508–518.

    Google Scholar 

  108. KASACK, U., Korrelationsempfang von Buchstaben in binärer bzw. ternärer Darstellung bei Bandbegrenzungen und gaußschem Rauschen, Archiv elek. Übertragung 22 (1968), 487–493.

    Google Scholar 

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Harmuth, H.F. (1969). Signal Design for Improved Reliability. In: Transmission of Information by Orthogonal Functions. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13227-2_7

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