Construction of Minimizers

The goal is to develop a construction scheme for minimizers of the uncertainty principles developed in UNLocX. By “minimizer” we mean optimal waveforms with respect to the generalized Localization Measures. This construction schemes will include and generalize the construction principles for minimizing Heisenberg type inequalities and/or inequalities derived from entropy or ambiguity function formulations. Moreover, we aim at developing a construction-scheme for uncertainty minimizers in view of specific signal processing tasks (e.g. signal coding and signal analysis/understanding). Thus we shall provide construction principles for optimal waveforms in the sense of the task-oriented versions of uncertainty inequalities developed in the component Localization Measures.

We have the following aims: