Adaptive RID kernels which minimize time-frequency uncertainty

The reduced interference distribution (RID) satisfies many of the desirable properties of time-frequency distributions (TFDs), including reduced interference. Using simple rules, it is possible to define kernels which guarantee the RID properties. A primitive h(t) is the starting point for kernel design. Starting with this primitive h(t), one may evolve a RID which enjoys all of the desirable properties. In addition, RIDs designed by this means also exhibit scale invariance in addition to the time-shift invariance and frequency-shift invariance exhibited by members of Cohen's class relevant to these properties. Such RIDs also exhibit a property which we call information invariance. Information invariance is defined under Renyi's generalized information. Renyi information has been found to be a useful quantifier of resolution in TFDs wherein minimum values of Renyi information are related to maximum resolution of the signal components. In this paper, we show that h(t) may be adapted to minimize Renyi information and thus achieve very good time-frequency resolution.<
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