Skip to main content
  • 607 Accesses

Abstract

Signals and signal processing methods are treated mathematically through mathematical models. The very basic model is that of a mathematical function. For instance, optical signals are regarded as functions that specify relationship between physical parameters of wave fields such as intensity, and phase and parameters of the physical space such as spatial coordinates and/or of time. Fig. 2.1.1 provides classification of signals as mathematical functions and associated terminology.

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

Access this chapter

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
Hardcover Book
USD 169.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W. B. Davenport, W. L. Root, An introduction to the theory of random signals and noise, McGraw-Hill, N.Y., 1958

    Google Scholar 

  2. B. R. Frieden, Numerical Methods in Probability Theory and Statistics, in: Computers in Optical Research, Methods in Applications, B. R. Frieden, ed., Springer Verlag, N.Y., 1980

    Chapter  Google Scholar 

  3. A. Papoulis, Signal Analysis, McGraw-Hill, N.Y., 1977

    Google Scholar 

  4. J. M. Wozencraft, I. M. Jacobs, Principles of Communication Engineering, J. Wiley & Sons, N. Y., 1965

    Google Scholar 

  5. L.P. Yaroslaysky, The Theory of Optimal Methods for Localization of Objects in Pictures, In: Progress in Optics, Ed. E. Wolf, v. XX XII, Elsevier Science Publishers, Amsterdam, 1993

    Google Scholar 

  6. D. Gabor, A new microscopic principle, Nature, v. 161, 777–778, 1948

    Article  ADS  Google Scholar 

  7. D. Gabor, Theory of Communication, Journ. Of IEE, vol. 93, 1946, pp. 429–457

    Google Scholar 

  8. E.N. Leith, J. Upatnieks, New techniques in wavefront reconstruction, JOSA, v. 51, 1469–1473, 1961

    Google Scholar 

  9. Yu. N. Denisyuk, Photographic reconstruction of the optical properties of an object in its own scattered radiation field, Dokl. Akad. Nauk SSSR, v. 1444, 1275–1279

    Google Scholar 

  10. J.W. Goodman, Introduction to Fourier Optics, Second edition, McGraw-Hill, 1988

    Google Scholar 

  11. E.C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford, 1948

    Google Scholar 

  12. L. Mertz, Transformation in Optics, Wiley, N.Y., 1965

    Google Scholar 

  13. G. L. Rogers, Noncoherent Optical Processing, Wiley, N.Y., 1977

    Google Scholar 

  14. A. Lohmann, J. Opt. Soc. Am., vol. 55, 1555–1556, 1965

    Article  Google Scholar 

  15. A.S. Marathay, J. Opt. Soc. Am., vol. 4, 1861–1868

    Google Scholar 

  16. R. V. L. Hartley, “A more symmetrical Fourier analysis applied to transmission problems,” Proc. IRE, v. 30, 144–150 (1942)

    Article  MathSciNet  MATH  Google Scholar 

  17. R. Bracewell, Two-dimensional Imaging, Prentice Hall, 1995

    Google Scholar 

  18. J. Bertrand, P. Bertrand, J.-Ph. Ovarlez, The Mellin Transform, in: The Transforms and Applications Handbook, Ed. A.D. Poularikas, CRC Press, 1966

    Google Scholar 

  19. Janke, Emde, Loesh, Tafeln Hoeherer Functionen, 6 Aufgabe, B. G. Teubner Verlaggesellschaft, Stuttgart, 1960 ((see also http://functions.wolframcom)

  20. P. Baues, Optoelectronics, v. 1, 37 (1969)

    Google Scholar 

  21. S. A. Collins, J. Opt. Soc. Am., vol. 60, p. 1168 (1970)

    Article  Google Scholar 

  22. S. Abe, J.T. Sheridan, Opt. Commun., vol. 113, p. 385 (1995)

    Article  ADS  Google Scholar 

  23. V. Namias, The fractional order Foutier transform and its applications in quantum mechanics, J. Inst. Maths. Applies., v. 25, pp. 241–265, 1980

    Article  MathSciNet  MATH  Google Scholar 

  24. A. Lohmann, Fourier curious, in: International trends in Optics, vol. 2, ICO series, J. C, Dainty, ed., 1994

    Google Scholar 

  25. A. Lohmann, Image rotation, Wigner rotation and the fractional Fourier transform, J. Opt. Soc. Am., vol. A10, pp. 2181–2186 (1993)

    Google Scholar 

  26. P. Pellat-Finet, G. Bonnet, Fractional order Fourier transform and Fourier optics, Opt. Comm., 111, 141 (1994)

    Article  ADS  Google Scholar 

  27. H. M. Ozaktas, Z. Zalevsky, M. A. Kutay, The Fractional Fourier Transform, with application in Optics and Signal Processing, Wiley, N. Y., 2000

    Google Scholar 

  28. CRC Handbook of Mathematical Sciences, 6th Edition, W. H. Beyer, Editor, CRC Press, Roca Baton, 1978

    Google Scholar 

  29. H. Barrett, The Radon Transform and its Applications, In: Progress in Optics, ed. By E. Wolf, Elsevier, Amsterdam, vol. 21, pp. 219–286, 1984,.

    Google Scholar 

  30. S. R. Deans, Radon and Abel Transforms, in: The Transforms and Applications Handbook, Ed. A.D. Poularikas, CRC Press, 1966

    Google Scholar 

  31. Y. Meyer, Wavelets: Algorithms and Applications, SIAM, 1993

    Google Scholar 

  32. S. G. Mallat, A theory for multiresolution signal decomposition: The wavelet representation, IEEE Trans. Pattern Anal. Machine Intell., PAMI-31, pp. 674–693, 1989

    Google Scholar 

  33. S. Mallat, A Wavelet Tour of Signal Processing, 2nd edition, Academic Press, 1999

    Google Scholar 

  34. M. Vetterli, J. Kovacevic, Wavelets and subband coding, Prentice Hall, Englewood Cliffs, N.J., 1995

    MATH  Google Scholar 

  35. A. Haar, Zur theorie der orthogonalen funktionensysteme, Math. Annal., Vol. 69,pp. 331–371, 1910

    Article  MathSciNet  MATH  Google Scholar 

  36. A. Papoulis, Probability, Random Variables and Stochastic Processes, McGrow-Hill, N.Y., 1984

    MATH  Google Scholar 

  37. J.W. Goodman. Statistical Properties of Laser Speckle Patterns, In: Laser Speckle and related Phenomena, J. C. Dainty, Ed., Springer Verlag, Berlin, 1975

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science+Business Media New York

About this chapter

Cite this chapter

Yaroslavsky, L. (2004). Optical Signals and Transforms. In: Digital Holography and Digital Image Processing. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4988-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-4988-5_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5397-1

  • Online ISBN: 978-1-4757-4988-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics