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Radomir S.Stankovic – Fournier Analysis on Finite Groups
Discover applications of Fourier analysis on finite non-Abelian groups
The majority of publications in spectral techniques consider Fourier transform on Abelian groups. However, non-Abelian groups provide notable advantages in efficient implementations of spectral methods. A solid foundation of this complex topic is provided by beginning with a review of signals and their mathematical models and Fourier analysis. Next, the book examines recent achievements and discoveries in:
- Matrix interpretation of the fast Fourier transform
- Optimization of decision diagrams
- Functional expressions on quaternion groups
- Gibbs derivatives on finite groups
- Linear systems on finite non-Abelian groups
- Hilbert transform on finite groups
Among the highlights is an in-depth coverage of applications of abstract harmonic analysis on finite non-Abelian groups in compact representations of discrete functions. Related tasks in signal processing and system design, including logic design. All chapters are self-contained, each with a list of references to facilitate the development of specialized courses or self-study.
With nearly 100 illustrative figures and fifty tables. This is an excellent textbook for graduate-level students and researchers in signal processing, logic design, and system theory-as well as the more general topics of computer science and applied mathematics.
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