We find coefficients such that for an arbitrary frame the set of vectors will again be a frame. Appropriate coefficients can always be chosen as function values ), where belongs to a broad class of functions generating a Gabor frame for . We also prove a version of the splitting trick, which allows to construct a large family of frames based on a single (wavelet or Gabor) frame.
Cite this article
Ole Christensen, Linear Combinations of Frames and Frame Packets. Z. Anal. Anwend. 20 (2001), no. 4, pp. 805–815DOI 10.4171/ZAA/1046