Spectral Representations for Quantized Chemical Signals

  • Russell D. Larsen
Part of the Modern Analytical Chemistry book series (MOAC)


A cardinal precept of management theory is that innovation comes from the outside. What, of relevance, can a spectroscopist learn from related disciplines? In this chapter we attempt to show how some well-known ideas in statistics, mathematics, and electrical engineering contribute to a better understanding of what a spectroscopist is attempting to measure, how certain traditional data-handling techniques are special cases of more general mathematical methods, and how modern signal-processing techniques relate to specific chemical signals. Most of the concepts in this chapter will be illustrated by application to FT NMR, in which the primary measured quantity is the free-induction decay signal (FID). The illustrations involve 13C FIDs but the techniques are applicable to other nuclei as well. In addition, most of what follows applies to FT-IR and the transform techniques discussed in the earlier chapters of this book.


Spectral Representation Fourier Spectrum Automatic Speech Recognition Hadamard Matrice Zero Crossing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. H. Koopmans, The Spectral Analysis of Time Series, Academic Press, New York, 1974.Google Scholar
  2. 2.
    D. R. Brillinger, Time Series Data Analysis and Theory, Holt, Rinehart and Winston, New York, 1975.Google Scholar
  3. 3.
    R. R. Ernst and W. A. Anderson, Application of Fourier transform spectroscopy to magnetic resonance, Rev. Sci. Instrum. 37, 93 (1966).CrossRefGoogle Scholar
  4. 4.
    H. F. Harmuth, Transmission of Information by Orthogonal Functions, 2nd ed., Springer-Verlag, New York, 1972.CrossRefGoogle Scholar
  5. 5.
    N. Ahmed and K. R. Rao, Orthogonal Transforms for Digital Signal Processing, Springer-Verlag, New York, 1975.CrossRefGoogle Scholar
  6. 6.
    J. L. Walsh, A closed set of orthogonal functions, Am. J. Math. 45, 5 (1923).CrossRefGoogle Scholar
  7. 7.
    R. D. Larsen and W. R. Madych, Walsh-like expansions and Hadamard matrices, IEEE Trans. Acoust. Speech, Sig. Processing 24, 71 (1976).CrossRefGoogle Scholar
  8. 8.
    W. R. Madych, R. D. Larsen, and E. F. Crawford, Piecewise polynomial expansions, IEEE Trans. Acoust., Speech, Sig. Processing 25, 579 (1977).CrossRefGoogle Scholar
  9. 9.
    R. J. Niederjohn, A mathematical formulation and comparison of zero-crossing analysis techniques which have been applied to automatic speech recognition, IEEE Trans. Acoust., Speech, Sig. Processing 23, 373 (1975).CrossRefGoogle Scholar
  10. 10.
    P. C. Jain and N. M. Blachman, Detection of a PSK signal transmitted through a hard-limited channel, IEEE Trans. Inform. Theory 19, 623 (1973).CrossRefGoogle Scholar
  11. 11.
    B. Saltzberg, R. J. Edwards, R. G. Heath, and N. R. Burch, Synoptic analysis of EEG signals, in: Data Acquisition and Processing in Biology and Medicine (K. Enslein, ed.), Vol. 5, p. 267, Pergamon, Oxford, 1968.Google Scholar
  12. 12.
    J. C. R. Licklider and I. Pollack, Effects of differentiation, integration, and infinite peak clipping upon the intelligibility of speech, J. Acoust. Soc. Am. 20, 42 (1948).CrossRefGoogle Scholar
  13. 13.
    F. E. Bond and C. R. Cahn, On sampling the zeros of bandwidth-limited signals, IRE Trans. Inform. Theory 4, 110 (1958).CrossRefGoogle Scholar
  14. 14.
    M. Hinich, Estimation of spectra after hard clipping of gaussian processes, Technometrics 9, 391 (1967).Google Scholar
  15. 15.
    H. B. Voelcker, Toward a unified theory of modulation. Part I: Phase-envelope relationships, Proc. IEEE 54, 340 (1966); Part II: Zero manipulation, 54, 735 (1966).CrossRefGoogle Scholar
  16. 16.
    I. Bar-David, Sample functions of a gaussian process cannot be recovered from their zero crossings, IEEE Trans. Inform. Theory 21, 86 (1975).CrossRefGoogle Scholar
  17. 17.
    A. A. G. Requicha, Contributions to a Zero-Based Theory of Band-Limited Signals, Ph.D. Dissertation, University of Rochester, 1970.Google Scholar
  18. 18.
    S. O. Rice, Mathematical analysis of random noise, in: Selected Papers on Noise and Stochastic Processes (N. Wax, ed.), p. 133, Dover, New York, 1954.Google Scholar
  19. 19.
    J. Van Vleck, The spectrum of clipped noise, Radio Research Laboratory Report No. 51, Harvard Univ., 1943.Google Scholar
  20. 20.
    I. J. Good, The loss of information due to clipping a waveform, Inform. Control 10, 220 (1967).CrossRefGoogle Scholar
  21. 21.
    E. Masry, The recovery of distorted bandlimited stochastic processes, IEEE Trans. Inform. Theory 19, 398 (1973).CrossRefGoogle Scholar
  22. 22.
    I. Bar-David, An implicit sampling theorem for bounded bandlimited functions, Inform. Control 24, 36 (1974).CrossRefGoogle Scholar
  23. 23.
    H. B. Voelcker and A. A. G. Requicha, Clipping and signal determinism: Two algorithms requiring validation, IEEE Trans. Comm. 21, 738 (1973).CrossRefGoogle Scholar
  24. 24.
    A. Sekey, A computer simulation study of real-zero interpolation, IEEE Trans. Audio Electroacoust. 18, 43 (1970).CrossRefGoogle Scholar
  25. 25.
    R. D. Larsen and E. F. Crawford, Clipped free induction decay signal analysis, Anal. Chem. 49, 508 (1977).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1978

Authors and Affiliations

  • Russell D. Larsen
    • 1
  1. 1.Department of ChemistryUniversity of Nevada-RenoRenoUSA

Personalised recommendations