Skip to main content
SpringerLink
Log in

Some properties of the point processes generated by integral density modulation of renewal processes

  • Published:
Kybernetik Aims and scope Submit manuscript

Abstract

Integral density modulation of point processes is defined, and the properties of the modulated point processes are described. When a homogeneous renewal process is modulated by a step random signal, the mathematical expressions are derived of the probability density functions of the sums of r-successive inter point intervals, the intensity functions and the first order correlation coefficient of intervals. These quantities are calculated and illustrated for several parameter values. Modulated point sequences are generated by computer simulation method. The interval histograms and the serial correlation coefficients of counts and of intervals of the sequences are obtained. The results are compared with the theoretical results on the point processes modulated by the step random signal.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

IDM:

Integral density modulation

SRS:

Step random signal

PP:

Point process

PS:

Point sequence

PDF:

Probability density function

CPDF:

Conditional probability density function

JCPDF:

Joint conditional probability density function

SED:

Special Earlangian distribution

SCC:

Serial correlation coefficients

SIC:

Serial intensity coefficients

References

  • Cox, D.R., Lewis, P.A.W.: The statistical analysis of series of events, Chapter 4. London: Methuen 1966

    Google Scholar 

  • Cox, D.R.: The statistical analysis of dependencies in point processes, in Stochastic point processes (Lewis, P.A.W., Ed.). New York, London: Wiley 1972

    Google Scholar 

  • Eccles, J.C.: The physiology of synapses, Chapter 3. Berlin, Göttingen, Heidelberg, New York: Springer 1964

    Google Scholar 

  • Iso, Y., Yanaru, T., Nakayama, Y.: Some properties of the density modulated Poisson pulse trains, in Japanese. JJME 9, 406–412 (1971)

    Google Scholar 

  • Macchi, O.: Stochastic point processes and multicoincidences. IEEE Trans. Inf. 17, No. 1, 2–7 (1971)

    Google Scholar 

  • Nakahama, H., Ishii, N., Yamamoto, N.: A statistical analysis of spontaneous activity of central single neuron. Physiol. Behav. 3, 745–752 (1968)

    Google Scholar 

  • Nakahama, H., Ishii, N., Yamamoto, N.: Stochastic properties of spontaneous inpulse activity in central single neurons. Tohoku. J. 104, 373–409 (1971)

    Google Scholar 

  • Stratonovich, R.L.: Topics in the theory of random noise. New York, London: Gordon and Breach 1963

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics, Kyushu Institute of Technology, Kitakyushu, Japan

    Torao Yanaru & Yasuyuki Iso

Authors
  1. Torao Yanaru
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yasuyuki Iso
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yanaru, T., Iso, Y. Some properties of the point processes generated by integral density modulation of renewal processes. Kybernetik 16, 9–25 (1974). https://doi.org/10.1007/BF00270291

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00270291

Keywords

Search

Navigation