Chirp hunting

Chirplet Approximation of Band-Limited, Real Signals Made Easy

“…A sampling of the literature on this subject may be found in [1,2,7,8,9,10,11,14,15] and the references contained therein. The central problem in establishing such a formula is an efficient and natural method for obtaining the parameters characterizing the chirps.…”

“…The main drawback in the setup of chirp decomposition techniques is the weight of the computational effort required: according to the literature, most of the algorithms rely on matching pursuit techniques [12] where one first considers a rather complete dictionary of chirps in order to find iteratively the ones matching the signal as best as possible (see [1,4,7,9,10,11,14] and the recent paper [2] motivated by gravitational waves detection). However, in a very recent paper, Greenberg and co-authors [6] proposed a completely different approach where one gets rid of the dictionary and constructs the chirp approximation by means of a simple and easy-to-implement procedure.…”

Feature Extraction From Underwater Signals Using Time-Frequency Warping Operators

“…For each branch, the signal approximation by chirplet function (MPCE) is represented in the middle subplots. Each warped signal will be approximated by eight chirplet functions using the algorithm proposed in [28].…”

Cramer-Rao lower bounds for atomic decomposition

“…In a previous paper [1] we presented a method for atomic decomposition with chirped, Gabor functions based on maximum likelihood estimation. In this paper we present the Cramér-Rao lower bounds for estimating the seven chirp parameters, and the results of a simulation showing that our sub-optimal, but computationally tractable, estimators perform well in comparison to the bound at low signal-to-noise ratios.…”

“…In [1] we presented a method for obtaining this decomposition based on the principles of maximum likelihood estimation which we will briefly review in the next section. We will then present the Cramér-Rao lower bounds along with estimates of the mean and variance of the estimators proposed in [1].…”