22/10/2007

This webpage is linked to the paper

- P. Balazs, Hilbert-Schmidt Operators and Frames - Classification, Approximation by Multipliers and Algorithms, , International Journal of Wavelets, Multiresolution and Information Processing, (2007, accepted), preprint

- Find the best Approximation of a matrix by a frame multiplier: ApprFramMult (T,D,Ds).
- Build the matrix for a frame multiplier: FramMultMat(s,D,Ds)
- Two simple examples for the best approximation by frame multipliers: testapprframmult
- Find the best approximation of a frame multiplier by a frame multiplier: testapprframmult2
- Test the approximation of matrices by filters, Gabor and wavelet mulitpliers: TestBestApprMult
- Approximation of Matrices by irregular Gabor multiplier: GMAPPir
- Creates the irregular Gabor frame n the lattice xpo: Gabbaspir
- Create a synthesis matrix containing mexican hat wavelets: waveletmat
- Find the best approximation by circulant matrices: bestapprcircl

- Calculation of cross-Gram Matrix for Gabor systems : HSGramMatrXXL
- Fourier Transformation of a matrix FMFxxl

- Inverse Fourier Transformation of a matrix: iFMFxxl
- Creation of a translation matrix: transmatxxl

- All codes collected in one ZIP-file.

- Using the algorithm for approximation with frame multipliers in
the time invariant filter, Gabor and wavelet case.

- The time frequency spread of the best approximations in the last
figure.

Top Left: original system, Top Right: approximation by circulant matrices, i.e. time-invariant filters, Bottom Left: Gabor case, Bottom Right:wavelet case