Skip to main content
SpringerLink
Log in
Book cover

Transmission of Information by Orthogonal Functions pp 316–366Cite as

Signal Design for Improved Reliability

  • Chapter

  • 104 Accesses

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 response of attenuation and phase shift. For instance, the famous theorem by Nyquist [1] states that one independent symbol may be transmitted per time interval of duration Δ through an idealized frequency low-pass filter of bandwidth Δf, where

$$\tau = 1/2\Delta f$$
((1))

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

7.1.1

  1. Nyquist, H.: Certain topics in telegraph transmission theory.Trans. AIEE 47 (1928) 617–644.

    Google Scholar 

  2. Hartley, R.V.L.: Transmission of information.Bell System Tech. J. 7 (1928) 535–563.

    Google Scholar 

  3. Küpfmüller, K.:Die Systemtheorie der elektrischen Nachrichtenübertragung. Stuttgart: Hirzel, 1952.

    Google Scholar 

  4. Shannon, C.E.: A mathematical theory of communication.Bell System Tech. J. 27 (1948) 379–423, 623–656.

    MathSciNet  MATH  Google Scholar 

  5. Shannon, CE: Communication in the presence of noise.Proc. IRE 37 (1949) 10–21.

    Article  MathSciNet  Google Scholar 

7.1.2

  1. Fano, R.M.:Transmission of information. New York: MIT Press and Wiley, 1961.

    Google Scholar 

  2. Fey, P.:Informationstheorie. Berlin: Akademie-Verlag, 1963.

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  4. Madelung, E.:Die mathematischen Hilfsmittel des Physikers. Berlin/Göttingen/ Heidelberg: Springer, 1957.

    MATH  Google Scholar 

7.1.3

  1. Harmuth, H.: Die Übertraguñgskapazität von Nachrichtenkanälen nach der Verallgemeinerung des Begriffes Frequenz.Arch, elektr. Übertragung 19 (1965) 125–133.

    Google Scholar 

  2. Sommerfeld, A.: Über die Fortpflanzung des Lichtes in dispergierenden Medien.Ann. Phys. 44 (1914) 177–202.

    Article  Google Scholar 

7.2.1

  1. Davenport, W.B., Jr., Root, W.L.:An introduction to the theory of random signals and noise. New York: McGraw-Hill, 1958.

    MATH  Google Scholar 

  2. Harman, W.W.:Principles of the statistical theory of communication. New York: McGraw-Hill, 1963.

    MATH  Google Scholar 

  3. Wainstein, L.A., Zubakov, V.D.:Extraction of signals from noise. Englewood Cliffs, N.J.: Prentice Hall, 1962.

    Google Scholar 

7.2.2

  1. Harmuth, H., Schmid, P.E., Dudley, H.S.: Multiple access communication with binary orthogonal sine and cosine pulses using heavy amplitude clipping.1968 IEEE Int. Conf. on Communication, Record, pp. 794–799.

    Google Scholar 

  2. van Vleck, J.H., Middleton, D.: The spectrum of clipped noise.Proc. IEEE 54 (1966) 2–19.

    Article  Google Scholar 

  3. Sunde, E.D.: Ideal binary pulse transmission by AM and FM.Bell System Tech. J. 38 (1959) 1357–1426.

    Google Scholar 

  4. Harmuth, H., Schmid, P.E., Dudley, H.S.: Multiple access communication with binary orthogonal sine and cosine pulses using heavy amplitude clipping.IEEE Trans. Communication Technology COM-19 (1971) 1247–1252.

    Article  Google Scholar 

7.2.3

  1. Aikens, A.J., Lewinski, D.A.: Evaluation of message circuit noise.Bell System Tech. J. 39 (1960) 879–909.

    Google Scholar 

  2. Smith, D.B., Bradley, W.E.: The theory of impulse noise in ideal frequency-modulation receivers.Proc. IRE 34 (1946) 743–751.

    Article  Google Scholar 

  3. Bennett, W.R.:Electrical noise. New York: McGraw-Hill, 1960.

    Google Scholar 

  4. Stumpers, F.L.: On the calculation of impulse-noise transients in frequency-modulation receivers.Philips Research Reports 2 (1947) 468–474.

    MathSciNet  Google Scholar 

  5. Harmuth, H.: Kodieren mit orthogonalen Funktionen.Arch, elektr. Übertragung 17 (1963) 429–437, 508–518.

    Google Scholar 

7.3.1

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

    MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  3. Wozencraft, J.M., Reiffen, B.:Sequential decoding. New York: MIT Press and Wiley, 1961.

    MATH  Google Scholar 

  4. Gallager, R.G.:Low-density parity-check codes. Cambridge, Mass.: MIT Press, 1963.

    Google Scholar 

  5. Muller, D.E.: Application of Boolean algebra to switching circuit design and to error detection.IRE Trans. Electronic Computers EC-3 (1954) 6–12.

    Google Scholar 

  6. Peterson, W.W.:Error correcting codes. New York: MIT Press and Wiley, 1961.

    MATH  Google Scholar 

  7. Peterson, WW: Progress of information theory 1960–63.IEEE Trans. Information Theory IT-10 (1963) 221–264.

    Google Scholar 

  8. Lee, C.Y.: Some properties of non-binary error correcting codes.IRE Trans. Information Theory IT-4 (1958) 72–82.

    Google Scholar 

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

    Google Scholar 

  10. Reed, I. S.: A class of multiple-error-correcting codes and the decoding scheme.IRE Trans. Information Theory IT-4 (1954) 38–49.

    Article  Google Scholar 

  11. Weiss, P.: Über die Verwendung von Walshfunktionen in der Codierungs-theorie.Arch, elektr. Übertragung 21 (1967) 255–258.

    Google Scholar 

  12. Pearl, J.: Walsh processing of random signals.Proc. 1971 Walsh Functions Symposium, 137–141.

    Google Scholar 

  13. Helm, H. A.: Group codes and Walsh functions.Proc. 1971 Walsh Functions Symposium, 78–83.

    Google Scholar 

  14. Pearl, J.: Application of Walsh transform to statistical analysis.IEEE Trans. Systems, Man and Cybernetics SMC-1 (1971) 111–119.

    Article  Google Scholar 

7.3.2

  1. Golomb, S.W., Baumert, L.D., Easterling, M.F., Stiffler, J.J., Viterbi, A.J.:Digital communications. Englewood Cliffs, N.J.: Prentice Hall, 1964.

    MATH  Google Scholar 

  2. Harmuth, H.: Orthogonal codes.Proc. IEE 107 C (1960) 242–248.

    MathSciNet  Google Scholar 

  3. Aronstein, R.H.: Comparison of orthogonal and block codes.Proc. IEE 110 (1963) 1965 - 1967.

    Google Scholar 

  4. Hsieh, P., Hsiao, M.Y.: Several classes of codes generated from orthogonal functions.IEEE Trans. Information Theory IT-10 (1964) 88–91.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  6. Lachs, G.: Optimization of signal waveforms.IEEE Trans. Information Theory IT-9 (1963) 95–97.

    Article  Google Scholar 

  7. Neidhardt, P.:Informationstheorie und automatische Informationsverarbeitung. Berlin: Verlag Technik, 1964.

    Google Scholar 

7.3.3

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

    Google Scholar 

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

    Google Scholar 

  3. The Rand Corporation:A Million random digits with 100000 normal deviates. Glencoe, Ill.: The Free Press, 1955.

    Google Scholar 

  4. Peterson, W.W.:Error correcting codes. New York: MIT Press and Wiley, 1961.

    MATH  Google Scholar 

  5. Elias, P.: Error-free coding.IRE Trans. Information Theory IT-4 (1954) 29–37.

    Article  MathSciNet  Google Scholar 

7.3.4

  1. Harmuth, H.: Kodieren mit orthogonalen Funktionen, II. Kombinations-Alphabete und Minimum-Energie-Alphabete.Arch, elektr. Übertragung 17 (1963) 508–518.

    Google Scholar 

  2. Kasack, U.: Korrelationsempfang von Buchstaben in binärer bzw. ternärer Darstellung bei Bandbegrenzungen und gauBschem Rauschen.Arch, elektr. Übertragung 22 (1968) 487–493.

    Google Scholar 

  3. Harmuth, H.:Transmission of information by orthogonal functions. 1st ed. New York/Heidelberg/Berlin: Springer, 1969.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, The Catholic University of America, Washington D.C., USA

    Dr. Henning F. Harmuth (Consulting Engineer and Adjunct Associate Professor)

Authors
  1. Dr. Henning F. Harmuth
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1972 Springer-Verlag, Berlin · Heidelberg

About this chapter

Cite this chapter

Harmuth, H.F. (1972). Signal Design for Improved Reliability. In: Transmission of Information by Orthogonal Functions. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61974-8_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-61974-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-61976-2

  • Online ISBN: 978-3-642-61974-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation