Systematic construction of real lapped tight frame transforms

Aliaksei Sandryhaila, Amina Chebira, Christina Milo, Jelena Kovačević, Markus Püschel

Research output: Contribution to journalArticlepeer-review

Abstract

We present a constructive algorithm for the design of real lapped equal-norm tight frame transforms. These transforms can be efficiently implemented through filter banks and have recently been proposed as a redundant counterpart to lapped orthogonal transforms, as well as an infinite-dimensional counterpart to harmonic tight frames. The proposed construction consists of two parts: First, we design a large class of new real lapped orthogonal transforms derived from submatrices of the discrete Fourier transform. Then, we seed these to obtain real lapped tight frame transforms corresponding to tight, equal-norm frames. We identify those frames that are maximally robust to erasures, and show that our construction leads to a large class of new lapped orthogonal transforms as well as new lapped tight frame transforms.

Original languageEnglish (US)
Article number5401080
Pages (from-to)2556-2567
Number of pages12
JournalIEEE Transactions on Signal Processing
Volume58
Issue number5
DOIs
StatePublished - May 2010

Keywords

  • Bases
  • DFT
  • Filter banks
  • Frames
  • Lapped orthogonal transforms
  • Orthonormal
  • Paraunitary matrices
  • Tight

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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