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Gabor Frames in ℓ2(ℤ)

  • Ole Christensen
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Every numerical calculation with functions in L 2(ℝ) will involve a discrete model, where all calculations are done with (finite) sequences in 2(ℤ). Therefore it is important to know that certain conditions on a Gabor frame {(E mb T na g} m,n ∈ℝ in fact imply that we can construct a frame for 2(ℤ) having a similar structure. The relevant conditions were discovered by Janssen, and the main part of this chapter will deal with his results.

One can also consider frames in 2(ℤ) with a Gabor-like structure without referring to frames in L 2(ℝ). The theory for these frames is very similar to the Gabor theory in L 2(ℝ) and will not be discussed in detail.

Keywords

Filter Bank Tight Frame Dual Frame Gabor Frame Lebesgue Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Ole Christensen
    • 1
  1. 1.Department of MathematicsTechnical University of DenmarkLyngbyDenmark

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