Gabor Frames in ℓ2(ℤ)

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


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.


Filter Bank Tight Frame Dual Frame Gabor Frame Lebesgue Point 
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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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