Vandermonde factorization of Toeplitz matrices and applications in filtering and warping
Open accessAbstract
By deriving a factorization of Toeplitz matrices into the product of Vandermonde matrices, we demonstrate that the Euclidean norm of a filtered signal is equivalent with the Euclidean norm of the appropriately frequency-warped and scaled signal. In effect, we obtain an equivalence between the energy of frequency-warped and filtered signals. While the result does not provide tools for warping per se, it does show that the energy of the warped signal can be evaluated efficiently, without explicit and complex computation of the warped transform. The main result is closely related to the Vandermonde factorization of Hankel matrices.
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- Authors
- Backstrom, T.
- Affiliations
- International Audio Laboratories Erlangen, Friedrich Alexander University of Erlangen-Nürnberg (FAU) and Fraunhofer Institute of Integrated Circuits, IIS, Erlangen, Germany
- Venue
- IEEE Transactions on Signal Processing
- Published
- 2013-12
- Volume
- 61
- Issue
- 24
- Pages
- 6257-6263
- ISSN
- 1053-587X (ISSN-L)
- 1941-0476
- OpenAlex
- W2051356723
- Cited by
- 26
- References
- 16
- Citations by year
- 2025: 1 · 2024: 5 · 2023: 2 · 2022: 2 · 2021: 1 · 2020: 2 · 2019: 2 · 2018: 1 · 2017: 4 · 2016: 1 · 2015: 1 · 2014: 3 · 2013: 1
- FWCI
- 3.07
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- IEEE Transactions on Signal Processing (publishedVersion)
- Fraunhofer-Publica (Fraunhofer-Gesellschaft) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Keywords
- Toeplitz matrices, Vandermonde matrix, frequency warping, signal filtering, energy equivalence, L2 norm, Hankel matrices
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