Renyi information and signal-dependent optimal kernel design

The Renyi uncertainty measure has been proposed to be a measurement of complexity of signals. We further suggest that it can be used to evaluate the performance of different time-frequency distributions (TFDs). We provide two schemes of normalization in calculating the Renyi uncertainty measure. For the first one, TFDs are normalized by their energy, while for the second one, normalized with their volume. The behavior of the Renyi uncertainty measure under several situations is studied. A signal-dependent algorithm is developed to achieve TFDs with a minimal uncertainty measure. For the first normalization scheme, the Wigner distribution is found to be optimal or near-to-optimal under certain constraints. If the second scheme is used, our program can generate minimum uncertainty product kernels which are very effective at suppressing cross terms and maintaining high resolution.