Fourier Analysis on Finite Grs with Applications in Signal by Radomir S. Stankovic, Claudio Moraga, Jaakko Astola

By Radomir S. Stankovic, Claudio Moraga, Jaakko Astola

Discover functions of Fourier research on finite non-Abelian teams

the vast majority of guides in spectral options contemplate Fourier rework on Abelian teams. notwithstanding, non-Abelian teams offer amazing merits in effective implementations of spectral tools.

Fourier research on Finite teams with functions in sign Processing and procedure layout examines elements of Fourier research on finite non-Abelian teams and discusses diverse equipment used to figure out compact representations for discrete capabilities delivering for his or her effective realizations and similar functions. Switching capabilities are incorporated for example of discrete features in engineering perform. also, attention is given to the polynomial expressions and selection diagrams outlined when it comes to Fourier remodel on finite non-Abelian teams.

an effective beginning of this advanced subject is equipped via starting with a overview of signs and their mathematical versions and Fourier research. subsequent, the publication examines fresh achievements and discoveries in:

  • Matrix interpretation of the quick Fourier rework
  • Optimization of determination diagrams
  • Functional expressions on quaternion teams
  • Gibbs derivatives on finite teams
  • Linear structures on finite non-Abelian teams
  • Hilbert rework on finite teams

one of the highlights is an in-depth assurance of purposes of summary harmonic research on finite non-Abelian teams in compact representations of discrete services and similar projects in sign processing and method layout, together with good judgment layout. All chapters are self-contained, each one with a listing of references to facilitate the improvement of specialised classes or self-study.

With approximately a hundred illustrative figures and fifty tables, this can be a great textbook for graduate-level scholars and researchers in sign processing, common sense layout, and process theory-as good because the extra basic themes of laptop technological know-how and utilized arithmetic.

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Extra resources for Fourier Analysis on Finite Grs with Applications in Signal Processing and System Design

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Theory of Group Representations and Applications, Varszawa. 1977. 3. , Fourier-AnalysisandApproximation, Vol. I, Birkhauser Verlag, Base1 and Stuttgart, 1971. 4. , “A class of generalized functions”, facijic J. , 5 , 1955, 17-31. 5. , “An algorithm for machine calculation of complex Fourier series”, Math. Computation, Vol. 19, 1965, 297-301. 6. , Representation Theory of Finite Groups and Associative Algebras, Halsted, New York, London, 1962. 7. , “On the Walsh functions”, Trans. Amer: Math. , Vol.

Rept. quant-ph/0304064, Quantum Physics e-print Archive, 2003. 34. , “On a class of rearrangeable switching networks”, Bell System Tech. , SC, 1579-1618, 1971. 35. , “Sampling theorem with respect to Walsh-Fourier analysis”, Appendix B in Reports Walsh Functions and Linear System Theory, Elect. Eng. , Univ. of Maryland, College Park, MD, May 1970. 36. , “Some applications of generalized FFTs”, An appendix WID. ), Proc. ofthe DIMACS Workshop on Groups and Computation, June 7- 10, 1995, published 1997, 329-369.

However, in the case of Fourier transform on non-Abelian groups there are some important differences which must be appreciated at least in practical applications. According to this fact, our aim in this chapter is twofold. First, we consider a matrix representation of the fast Fourier transform on finite non-Abelian groups introduced in attempting to keep the entire analogy with the Abelian case as much as that is possible in the shape of the derived corresponding fast flow-graphs, and, then, we point out and discuss the main differences of this transform with respect to the fast Fourier transform on finite Abelian groups.

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