Estimating maxima of generalized cross ambiguity functions,and uncertainty principles |
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Authors: | Say Song Goh Tim N.T. Goodman |
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Affiliation: | 1. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore;2. Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, The University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom |
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Abstract: | In certain signal processing problems, it is customary to estimate parameters in distorted signals by approximating what is termed a cross ambiguity function and estimating where it attains its maximum modulus. To unify and generalize these procedures, we consider a generalized form of the cross ambiguity function and give error bounds for estimating the parameters, showing that these bounds are lower if we maximize the real part rather than the modulus. We also reveal a connection between these bounds and certain uncertainty principles, which leads to a new type of uncertainty principle. |
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