Skip to main content

The Method of Least Squares and Signal Analysis

  • Chapter
  • 3735 Accesses

Abstract

This chapter deals with three common problems in experimental science. The first is fitting a discrete set of experimental data with a mathematical function. The function usually has some parameters that must be adjusted to give a “best” fit. The second is to detect a periodic change in some variable—a signal—which may be masked by random changes—noise—superimposed on the signal. The third is to determine whether sets of apparently unsystematic data are from a random process or a process governed by deterministic chaotic behavior.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   79.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Adair, R. K., R. D. Astumian, and J. C. Weaver (1998). Detection of weak electric fields by sharks, rays and skates. Chaos. 8(3): 576–587.

    Article  ADS  Google Scholar 

  • Anderka, M., E. R. Declercq, and W. Smith (2000). A time to be born. Amer. J. Pub. Health 90(1): 124–126.

    Article  Google Scholar 

  • Astumian, R. D. (1997). Thermodynamics and kinetics of a Brownian motor. Science. 276: 917–922.

    Article  Google Scholar 

  • Astumian, R. D. and F. Moss (1998). Overview: The constructive role of noise in fluctuation driven transport and stochastic resonance. Chaos. 8(3): 533–538.

    Article  MATH  ADS  Google Scholar 

  • Bevington, P. R., and D. K. Robinson (1992). Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. New York, McGraw-Hill.

    Google Scholar 

  • Blackman, R. B., and J. W. Tukey (1958). The Measurement of Power Spectra. AT&T. New York, Dover, pp. 32–33.

    Google Scholar 

  • Bracewell, R. N. (1990). Numerical transforms. Science 248: 697–704.

    Article  ADS  MathSciNet  Google Scholar 

  • Cohen, A. (2000). Biomedical signals: Origin and dynamic characteristics; frequency-domain analysis. In J. D. Bronzino, ed. The Biomedical Engineering Handbook, 2nd. ed. Vol. 1. Boca Raton, FL, CRC, pp. 52-1–52-4.

    Google Scholar 

  • Cooley, J. W., and J. W. Tukey (1965). An algorithm for the machine calculation of complex Fourier series. Math. Comput. 119: 297–301.

    MathSciNet  Google Scholar 

  • DeFelice, L. J. (1981). Introduction to Membrane Noise. New York, Plenum.

    Google Scholar 

  • Feynman, R. P., R. B. Leighton and M. Sands (1963). The Feynman Lectures on Physics, Vol. 1, Chapter 46. Reading, MA, Addison-Wesley.

    Google Scholar 

  • Gammiatoni, L., P. Hänggi, P. Jung and F. Marchesoni (1998). Stochastic resonance. Rev. Mod. Phys. 70(1): 223–287.

    Article  ADS  Google Scholar 

  • Gatland, I. R. (1993). A weight-watcher's guide to least-squares fitting. Comput. Phys. 7(3): 280–285.

    Google Scholar 

  • Gatland, I. R., and W. J. Thompson (1993). Parameter bias estimation for log-transformed data with arbitrary error characteristics. Am. J. Phys. 61(3): 269–272.

    Article  ADS  Google Scholar 

  • Gingl, Z., L. B. Kiss, and F. Moss (1995). Non–dynamical stochastic resonance: Theory and experiments with white and arbitrarily coloured noise. Europhys. Lett. 29(3): 191–196.

    Article  ADS  Google Scholar 

  • Glass, L. (2001). Synchronization and rhythmic processes in physiology. Nature. 410(825): 277–284.

    Article  ADS  Google Scholar 

  • Guyton, A. C. (1991). Textbook of Medical Physiology, 8th ed. Philadelphia, Saunders.

    Google Scholar 

  • Kaiser, I. H. and F. Halberg (1962). Circadian periodic aspects of birth. Ann. N. Y. Acad. Sci. 98: 1056–1068.

    Article  Google Scholar 

  • Kaplan, D., and L. Glass (1995). Understanding Nonlinear Dynamics. New York, Springer.

    MATH  Google Scholar 

  • Lighthill, M. J. (1958). An Introduction to Fourier Analysis and Generalized Functions. Cambridge, England, Cambridge University Press.

    Google Scholar 

  • Lybanon, M. (1984). A better least-squares method when both variables have uncertainties. Am. J. Phys. 52: 22–26.

    Article  ADS  Google Scholar 

  • Mainardi, L. T., A. M. Bianchi, and S. Cerutti (2000). Digital biomedical signal acquisition and processing. In J. D. Bronzino, ed. The Biomedical Engineering Handbook, 2nd. ed. Vol. 1. Boca Raton, FL, CRC, pp. 53-1–53-25.

    Google Scholar 

  • Maughan, W. Z., C. R. Bishop, T. A. Pryor, and J. W. Athens (1973). The question of cycling of blood neutrophil concentrations and pitfalls in the analysis of sampled data. Blood. 41: 85–91.

    Google Scholar 

  • Milnor, W. R. (1972). Pulsatile blood flow. New Eng. J. Med. 287: 27–34.

    Article  Google Scholar 

  • Nedbal, L. and V. Březnia (2002). Complex metabolic oscillations in plants forced by harmonic irradiance. Biophys. J. 83: 2180–2189.

    Article  ADS  Google Scholar 

  • Nyquist, H. (1928). Thermal agitation of electric charge in conductors. Phys. Rev. 32: 110–113.

    Article  ADS  Google Scholar 

  • Orear, J. (1982). Least squares when both variables have uncertainties. Am. J. Phys. 50: 912–916.

    Article  ADS  Google Scholar 

  • Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (1992). Numerical Recipes in C: The Art of Scientific Computing, 2nd ed., reprinted with corrections, 1995. New York, Cambridge University Press.

    Google Scholar 

  • Visscher, P. B. (1996). The FFT: Fourier transforming one bit at a time. Comput. Phys. 10(5): 438–443.

    Article  ADS  Google Scholar 

  • Wiesenfeld, K. and F. Jaramillo (1998). Minireview of stochastic resonance. Chaos 8(3): 539–548.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer

About this chapter

Cite this chapter

Hobbie, R.K., Roth, B.J. (2007). The Method of Least Squares and Signal Analysis. In: Intermediate Physics for Medicine and Biology. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49885-0_11

Download citation

Publish with us

Policies and ethics