Frames and Orthonormal Bases for Variable Windowed Fourier Transforms.

Abstract

We generalize the windowed Fourier transform to the variable windowed Fourier transform. This generalization brings the Gabor transform and the wavelet transform under the same framework. Using frame theory we characterize frames and orthonormal bases for the variable windowed Fourier series (VWFS). These characterizations are formulated explicitly in terms of window functions. Therefore they can serve as guidelines for designing windows for the VWFS. We introduce the notion of 'complete orthogonal support' and, with the help of this notion, we construct a class of orthonormal VWFS bases for L(sq)(R+).

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Document Details

Document Type
Technical Report
Publication Date
Jul 29, 1996
Accession Number
ADA311766

Entities

People

  • Louis L. Scharf
  • Neng-tsann Ueng

Organizations

  • University of Colorado Boulder

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Colorado
  • Computers
  • Digital Signal Processing
  • Electrical Engineering
  • Engineering
  • Fourier Series
  • Frequency
  • Frequency Domain
  • Hilbert Space
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • Real Numbers
  • Sequences
  • Signal Processing
  • Universities
  • Wavelet Transforms

Readers

  • Calculus or Mathematical Analysis
  • Image Processing and Computer Vision.
  • Systems Analysis and Design