Abstract

We use the principles of maximum likelihood estimation to construct a method for decomposing signals into a weighted sum of chirped Gabor functions. This method provides a sparse representation of the signal similar to basis and matching pursuit methods. However since the parameters of the chirps are estimated rather than discretized, the "dictionary" is essentially of infinite size. Since the maximum likelihood estimator requires excessive computations, we propose sub-optimal estimators for the chirp parameters, and present a novel method for estimating chirp rate. 1. INTRODUCTION Given a signal, x(n), our goal is to find a sparse decomposition of the signal as a weighted sum of chirped Gabor functions x = x(n) = M X i=1 A i e jOE i s(n; t i ; ! i ; c i ; d i ); where s t;!;c;d = s(n; t; !; c; d) = i p 2ßd j \Gamma 1 2 exp n \Gamma \Gamma n\Gammat 2d \Delta 2 + j c 2 (n \Gamma t) 2 + j!(n \Gamma t) o : The parameters t, !, c, and d represent, respectively, the ...

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