Heisenberg's Inequality and Logarithmic Heisenberg's Inequality for Ambiguity Function |
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Authors: | Guji Tian |
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Abstract: | In this article we discuss the relation between Heisenberg's inequality and logarithmic Heisenberg's (entropy) inequality for ambiguity function. After building up a Heisenberg's inequality, we obtain a connection of variance with entropy by variational method. Using classical Taylor's expansion, we prove that the equality in Heisenberg's inequality holds if and only if the entropy of 2k - 1 order is equal to (2k - 1}!. |
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Keywords: | Heisenberg's inequality ambiguity function logarithmic Heisenberg's inequality entropy |
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