General frame theory can be more specialized if a structure is imposed on the elements of the frame in question. One possible, very natural structure is sequences of shifts of the same function. In this project, irregular shifts are investigated.
In this project, the connection to irregular Gabor multipliers will be explored. Using the Kohn Nirenberg correspondence, the space spanned by Gabor multipliers is just a space spanned by translates. Furthermore, the special connection of the Gramian function and the Grame matrix for this case will be investigated.
A typical example of frames of translates is filter banks, which have constant shapes. For example, the phase vocoder corresponds to a filter bank with regular shifts. Introducing an irregular shift gives rise to a generalization of this analysis / synthesis system.
- S. Heineken, Research Group on Real and Harmonic Analysis, University of Buenos Aires