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Sparse Representations with Chirplets via Maximum Likelihood Estimation
"... We formulate the problem of approximating a signal with a sum of chirped Gaussians, the socalled chirplets, under the framework of maximum likelihood estimation. For a signal model of one chirplet in noise, we formulate the maximum likelihood estimator (MLE) and compute the Cram'erRao lower bound. ..."
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We formulate the problem of approximating a signal with a sum of chirped Gaussians, the socalled chirplets, under the framework of maximum likelihood estimation. For a signal model of one chirplet in noise, we formulate the maximum likelihood estimator (MLE) and compute the Cram'erRao lower bound. An approximate MLE is developed, based on timefrequency methods, and is applied sequentially to obtain a decomposition of multiple chirplets. The decomposition is refined after each iteration with the expectationmaximization algorithm. A version of the algorithm, which is O(N) for each chirplet of the decomposition, is applied to a data set of whale whistles. I. Introduction Chirplets are a class of signals that consists of Gaussians that are translated in time and frequency, scaled, and chirped. They are defined as s t;!;c;d = s(n; t; !; c; d) = ( p 2d) \Gamma 1 2 exp n \Gamma \Gamma n\Gammat 2d \Delta 2 + j c 2 (n \Gamma t) 2 + j!(n \Gamma t) o : where t, !, and c...
Estimating Multiple FrequencyHopping Signal Parameters via Sparse Linear Regression
"... Abstract—Frequency hopping (FH) signals have welldocumented merits for commercial and military applications due to their nearfar resistance and robustness to jamming. Estimating FH signal parameters (e.g., hopping instants, carriers, and amplitudes) is an important and challenging task, but optimu ..."
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Abstract—Frequency hopping (FH) signals have welldocumented merits for commercial and military applications due to their nearfar resistance and robustness to jamming. Estimating FH signal parameters (e.g., hopping instants, carriers, and amplitudes) is an important and challenging task, but optimum estimation incurs an unrealistic computational burden. The spectrogram has long been the starting nonparametric estimator in this context, followed by line spectra refinements. The problem is that hop timing estimates derived from the spectrogram are coarse and unreliable, thus severely limiting performance. A novel approach is developed in this paper, based on sparse linear regression (SLR). Using a dense frequency grid, the problem is formulated as one of underdetermined linear regression with a dual sparsity penalty, and its exact solution is obtained using the alternating direction method of multipliers (ADMoM). The SLRbased approach is further broadened to encompass polynomialphase hopping (PPH) signals, encountered in chirp spread spectrum modulation. Simulations demonstrate that the developed estimator outperforms spectrogrambased alternatives, especially with regard to hop timing estimation, which is the crux of the problem. Index Terms—Compressive sampling, frequency hopping signals, sparse linear regression, spectrogram, spread spectrum signals. I.
A Window Width Optimized STransform
, 2008
"... Energy concentration of the Stransform in the timefrequency domain has been addressed in this paper by optimizing the width of the window function used. A new scheme is developed and referred to as a window width optimized Stransform. Two optimization schemes have been proposed, one for a constan ..."
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Energy concentration of the Stransform in the timefrequency domain has been addressed in this paper by optimizing the width of the window function used. A new scheme is developed and referred to as a window width optimized Stransform. Two optimization schemes have been proposed, one for a constant window width, the other for timevarying window width. The former is intended for signals with constant or slowly varying frequencies, while the latter can deal with signals with fast changing frequency components. The proposed scheme has been evaluated using a set of test signals. The results have indicated that the new scheme can provide much improved energy concentration in the timefrequency domain in comparison with the standard Stransform. It is also shown using the test signals that the proposed scheme can lead to higher energy concentration in comparison with other standard linear techniques, such as shorttime Fourier transform and its adaptive forms. Finally, the method has been demonstrated on engine knock signal analysis to show its effectiveness.