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Algorithmic Implementation

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Multidimensional Signals and Systems

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Abstract

This chapter takes a turn into the discrete world. While continuous multidimensional systems are and will be of practical importance, their modelling and simulation is accomplished by digital means. Therefore the description of continuous multidimensional systems is at first cast into a state space representation. Then the continuous-time representation is converted into discrete-time by so-called continuous-discrete conversion methods. Both steps, state space representation and time-discretization, lead to a general computational framework for the solution of initial-boundary-value problems.

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References

  1. Rabenstein, R., Schäfer, M.: Multidimensional Signals and Systems: Applications. Springer Nature, Heidelberg, Berlin (to appear)

    Google Scholar 

  2. Bronshtein, I., Semendyayev, K., Musiol, G., Mühlig, H.: Handbook of Mathematics. Springer-Verlag, Berlin (2015)

    Book  MATH  Google Scholar 

  3. Dunford, N., Schwartz, J.T.: Linear Operators, Part I General Theory. Wiley-Interscience, Hoboken, NJ (1988)

    Google Scholar 

  4. Dymkou, V., Pothérat, A.: Spectral methods based on the least dissipative modes for wall bounded mhd flows. Theoretical and Computational Fluid Dynamics 23(6), 535–555 (2009). https://doi.org/10.1007/s00162-009-0159-9

    Article  MATH  Google Scholar 

  5. Dymkou, V., Rabenstein, R., Steffen, P.: Discrete simulation of a class of distributed systems using functional analytic methods. Multidimensional Systems and Signal Processing 17(2), 177–209 (2006). https://doi.org/10.1007/s11045-005-6234-5

    Article  MathSciNet  MATH  Google Scholar 

  6. Dymkou, S.M., Dymkou, V.M., Dymkov, M.P.: Multifunctional transformation method in flow modeling. IFAC Proceedings Volumes 47(3), 7013–7018 (2014). https://doi.org/10.3182/20140824-6-ZA-1003.00777. http://www.sciencedirect.com/science/article/pii/S1474667016427163. 19th IFAC World Congress

  7. Franke, D.: Systeme mit örtlich verteilten Parametern. Eine Einführung in die Modellbildung, Analyse und Regelung. Hochschultext. Springer, Berlin u.a. (1987)

    Google Scholar 

  8. Gabel, R.A., Roberts, R.A.: Signals and Linear Systems, 3 edn. Wiley (1986)

    Google Scholar 

  9. Gilles, E.: Systeme mit verteilten Parametern: Einf. in d. Regelungstheorie. Methoden der Regelungstechnik. Oldenbourg (1973)

    Google Scholar 

  10. Jackson, L.B.: A correction to impulse invariance. IEEE Signal Processing Letters 7(10), 273–275 (2000)

    Article  Google Scholar 

  11. Kato, T.: Perturbation Theory for Linear Operators. Springer-Verlag, Berlin, Germany (1976)

    MATH  Google Scholar 

  12. Kowalczuk, Z.: Discrete approximation of continuous-time systems: a survey. IEE Proceedings G - Circuits, Devices and Systems 140(4), 264–278 (1993)

    Article  Google Scholar 

  13. Lathi, B.P., Green, R.A.: Essentials of Digital Signal Processing. Cambridge University Press, Cambridge, UK (2014). https://doi.org/10.1017/CBO9781107444454

  14. Leis, J.W.: Digital Signal Processing Using MATLAB for Students and Researchers. John Wiley & Sons, Ltd, Chichester, UK (2011)

    Book  Google Scholar 

  15. Mecklenbräuker, W.F.: Remarks on and correction to the impulse invariant method for the design of IIR digital filters. Signal Processing 80(8), 1687–1690 (2000). https://doi.org/10.1016/S0165-1684(00)00113-4. http://www.sciencedirect.com/science/article/pii/S0165168400001134

  16. Mitra, S.K.: Digital Signal Processing, 4 edn. McGraw-Hill, Boston, USA (2010)

    Google Scholar 

  17. Mitra, S.K., Kaiser, J.F.: Handbook for Digital Signal Processing. John Wiley & Sons Ltd., New York, USA (1993)

    MATH  Google Scholar 

  18. Oppenheim, A.V., Schafer, R.W.: Discrete-Time Signal Processing, 3 edn. Prentice Hall Signal Processing Series. Pearson (2010)

    Google Scholar 

  19. Schäfer, M., Rabenstein, R., Strobl, C.: A multidimensional transfer function model for frequency dependent transmission lines. In: 2017 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–4 (2017)

    Google Scholar 

  20. Schäfer, M., Schlecht, S.J., Rabenstein, R.: Feedback structures for a transfer function model of a circular vibrating membrane. In: Proc. IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), pp. 1–5. New Paltz, NY (2019)

    Google Scholar 

  21. Schüßler, H.W.: Digitale Signalverarbeitung 1. Springer, Berlin Heidelberg (2008)

    MATH  Google Scholar 

  22. Schüßler, H.W.: Digitale Signalverarbeitung 2. Springer, Berlin Heidelberg (2010)

    Book  Google Scholar 

  23. Smith III, J.O.: Physical Audio Signal Processing: for Virtual Musical Instruments and Digital Audio Effects. W3K Publishing (2010)

    Google Scholar 

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Authors and Affiliations

  1. Multimedia Communications and Signal Processing, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany

    Rudolf Rabenstein

  2. Digital Communications, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany

    Maximilian Schäfer

Authors
  1. Rudolf Rabenstein
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  2. Maximilian Schäfer
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Rabenstein, R., Schäfer, M. (2023). Algorithmic Implementation. In: Multidimensional Signals and Systems. Springer, Cham. https://doi.org/10.1007/978-3-031-26514-3_12

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  • DOI: https://doi.org/10.1007/978-3-031-26514-3_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-26513-6

  • Online ISBN: 978-3-031-26514-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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