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Pattern Analysis under Number Theoretic Transforms

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Computer Aided Systems Theory – EUROCAST 2011 (EUROCAST 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6928))

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Abstract

Number Theoretic Transforms (NTT) are integer-valued transforms that may be applied for signal processing. Particularly the Mersenne and the Fermat Transforms are interesting, since being close related to special powers of two, at the computational level, product operations needed for convolution may be efficiently reduced to shift operations. NTT exhibit, like the Fourier Transform, important properties, like the Convolution and Parseval theorems. In this paper however the focus will be on the analysis of geometric and chromatic changes on patterns using 2D-NTT.

Work leading to this paper was partially supported by the Foundation for the Advance of Soft Computing, Mieres, Asturias, Spain.

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References

  1. Agarwal, R.C., Burrus, C.S.: Fast convolution using Fermat number transforms with applications to digital filtering. IEEE Trans. Acoust. Speech Signal Processing 22, 87–97 (1974)

    Article  MathSciNet  Google Scholar 

  2. Barthel, A.: Betrachtung von zahlentheoretischen Transformationen auf Mustern, Diplomarbeit, Fakultät Informatik, Universität Dortmund (1992)

    Google Scholar 

  3. Leibowitz, L.M.: Exact Fermat number transform convolution with comparison to fast Fourier transform techniques. Dissertation, The George Washington University, Dept. Computer Science (1978)

    Google Scholar 

  4. Nicholson, P.J.: Algebraic theory of finite Fourier Transforms. Jr. Comput. Systems Sci. 5, 524–547 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  5. Pollard, J.M.: The fast Fourier Transform in a Finite Field. Math. Comput. 25, 365–374 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  6. Rader, C.M.: Discrete convolutions via Mersenne transforms. IEEE Trans. Computers 21, 1269–1273 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  7. Schönhage, A., Strassen, V.: Schnelle Multiplikation großer Zahlen. Computing 7, 281–292 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  8. Wikipedia, http://en.wikipedia.org/wiki/Number-theoretic_transform

  9. Walsh, J.L.: A closed set of orthogonal functions. Am. Jr. Math. 45, 2–5 (1923)

    MathSciNet  Google Scholar 

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Roberto Moreno-Díaz Franz Pichler Alexis Quesada-Arencibia

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Moraga, C. (2012). Pattern Analysis under Number Theoretic Transforms. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2011. EUROCAST 2011. Lecture Notes in Computer Science, vol 6928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27579-1_36

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  • DOI: https://doi.org/10.1007/978-3-642-27579-1_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27578-4

  • Online ISBN: 978-3-642-27579-1

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