Frame Transformation, Classification and Algorithms

created: 09/05/2006; last update:
03/12/2015

Update 2015:

The topic of frames in finite dimensional spaces is treated in much more details in

- Eds. P.G. Casazza and G. Kutyniok,
**Finite Frames: Theory and Applications**, Birkhäuser, Boston (2012)

The implementation for general frames can be found in

- Zdeněk Průša, Peter L. Søndergaard, Nicki Holighaus, Christoph Wiesmeyr, Peter Balazs
*The Large Time-Frequency Analysis Toolbox 2.0*. Sound, Music, and Motion, Lecture Notes in Computer Science 2014, pp 419-442

This webpage is linked to the paper

- P. Balazs, "Frames and Finite Dimensionality: Frame Transformation, Classification and Algorithms", Applied Mathematical Sciences, Vol. 2, no. 41-44, pp. 2131-2144, (2008) (preprint on arxiv),

- Build the synthesis matrix for the canonical dual frame: candualframe(D)

- Build the synthesis matrix for the canonical tight frame: cantightframe(D)
- Cross-Gram Matrix of two sequences: CrossGram(D1,D2)
- Calculate the framebounds of a frame: framebounds(D)

- Create random frame (in the unit circle): RandFrame(dim,M)
- Plot 2- and 3-dimensional frame: PlotFrame(D)
- Script for testing the frame transformation using stochastic parameters: testframtrans2
- Script for testing the frame transformation using fixed frames: testframtrans
- Arrowline 2-D and 3-D vector plot allowing colors and annotations: vectarrowxxl(p0,p1) [based on external code vectarrow(p0,p1)].
- All codes collected in one ZIP-file.

- Representation of the vectors of the frame (left) and its dual (right) of Example 3.1
- Representation of the vectors of the frame (left) and its dual
(right) of Example 3.2

R - Representation of the vectors of the frame (left) and its dual
(right) of Example 3.3 (numbers were manually added).