Efficient DFT Architectures Based Upon Symmetries

This paper presents an efficient discrete Fourier transform (DFT) approach based upon an eigenvalue decomposition method. The work is based on some recent results on DFT eigenvectors, expressed exactly (not numerically) with simple exponential terms, with a considerable number of elements constraine...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2006-10, Vol.54 (10), p.3829-3838
Main Authors: Erseghe, T., Cariolaro, G.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Computational complexity
Computer architecture
Constraints
Discrete Fourier transforms
Discrete Fourier transforms (DFTs)
eigenvalue decomposition
Eigenvalues
Eigenvalues and eigenfunctions
Eigenvectors
Exact sciences and technology
Fast Fourier transforms
fast Fourier transforms (FFTs)
Flexible printed circuits
Fourier transforms
fractional Fourier transforms
Information, signal and communications theory
Mathematical models
Matrix decomposition
Miscellaneous
Partitioning algorithms
Signal processing
Signal processing algorithms
Symmetry
Telecommunications and information theory
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Summary:This paper presents an efficient discrete Fourier transform (DFT) approach based upon an eigenvalue decomposition method. The work is based on some recent results on DFT eigenvectors, expressed exactly (not numerically) with simple exponential terms, with a considerable number of elements constrained to 0, and with a high degree of symmetry. The result provides a generalization of known fast Fourier transform (FFT) algorithms based upon a divide-and-conquer approach. Moreover, it can have interesting applications in the context of fractional Fourier transforms, where it provides an efficient implementation
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2006.880216