Vandermonde factorization of toeplitz matrices and applications in filtering and warping

Tom Backstrom*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

15 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number6601660
Pages (from-to)6257-6263
Number of pages7
JournalIEEE Transactions on Signal Processing
Volume61
Issue number24
DOIs
Publication statusPublished - 3 Dec 2013
MoE publication typeA1 Journal article-refereed

Keywords

  • Convolution
  • filtering
  • Hankel
  • line spectral frequencies
  • time-frequency analysis
  • Toeplitz
  • Vandermonde
  • warping

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