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Chirp Hunting
 In Proc. of the IEEE Int. Symp. on TimeFrequency and TimeScale Analysis
, 1998
"... 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 ar ..."
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Cited by 10 (3 self)
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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 suboptimal 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 ...
Adaptive TimeVarying Cancellation of Wideband Interferences in SpreadSpectrum Communications Based on TimeFrequency Distributions
 IEEE Trans. Signal Processing
, 1999
"... The aim of this paper is to propose an adaptive method for suppressing wideband interferences in spread spectrum (SS) communications. The proposed method is based on the timefrequency representation of the received signal from which the parameters of an adaptive timevarying interference excision ..."
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Cited by 6 (0 self)
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The aim of this paper is to propose an adaptive method for suppressing wideband interferences in spread spectrum (SS) communications. The proposed method is based on the timefrequency representation of the received signal from which the parameters of an adaptive timevarying interference excision filter are estimated. The approach is based on the generalized WignerHough transform as an effective way to estimate the instantaneous frequency of parametric signals embedded in noise. The performance of the proposed approach is evaluated in the presence of linear and sinusoidal FM interferences plus white Gaussian noise in terms of SNR improvement factor and bit error rate (BER).
Virtues and Vices of Quartic TimeFrequency Distributions
 in IEEE Trans. on Signal Processing
, 2000
"... We present results concerning three different types of quartic (fourth order) timefrequency distributions. First, we present new results on the recently introduced local ambiguity function, and show that it provides more reliable estimates of instantaneous chirp rate than the Wigner distribution. S ..."
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Cited by 2 (1 self)
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We present results concerning three different types of quartic (fourth order) timefrequency distributions. First, we present new results on the recently introduced local ambiguity function, and show that it provides more reliable estimates of instantaneous chirp rate than the Wigner distribution. Second, we introduce the class of quartic, shiftcovariant, timefrequency distributions, and investigate distributions that localize quadratic chirps. Finally, we present a shift covariant distribution of time and chirprate. I. Introduction T HE notion of a timefrequency distribution (TFD) [1], [2], [3] is inherently a concept that is not well defined [4]. A frequency is something that is measured over a period of time (e.g. how many times does the heart beat in a minute), and we would like to specify this frequency description at an instant of time (e.g. how fast is the heart beating right now). Nevertheless, TFD's have proven to be useful in many applications [5]. TFD's have been defin...
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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Cited by 2 (0 self)
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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...
IMPROVED HIDDEN MARKOV MODEL PARTIAL TRACKING THROUGH TIMEFREQUENCY ANALYSIS
"... In this article we propose a modification to the combinatorial hidden Markov model developed in [1] for tracking partial frequency trajectories. We employ the WignerVille distribution and Hough transform in order to (re)estimate the frequency and chirp rate of partials in each analysis frame. We es ..."
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In this article we propose a modification to the combinatorial hidden Markov model developed in [1] for tracking partial frequency trajectories. We employ the WignerVille distribution and Hough transform in order to (re)estimate the frequency and chirp rate of partials in each analysis frame. We estimate the initial phase and amplitude of each partial by minimizing the squared error in the timedomain. We then formulate a new scoring criterion for the hidden Markov model which makes the tracker more robust for nonstationary and noisy signals. We achieve good performance tracking crossing linear chirps and crossing FM signals in white noise as well as real instrument recordings. 1.
Optimum TimeFrequency Distribution for Detecting a DiscreteTime Chirp Signal in White Gaussian Noise
"... In the continuoustime domain, MaximumLikelihood (ML) detection of a chirp signal in white Gaussian noise can be done via the lineintegral transform of the classical Wigner distribution. The lineintegral transform is known variously as the Hough transform and the Radon transform. For discretetim ..."
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In the continuoustime domain, MaximumLikelihood (ML) detection of a chirp signal in white Gaussian noise can be done via the lineintegral transform of the classical Wigner distribution. The lineintegral transform is known variously as the Hough transform and the Radon transform. For discretetime signals, the Wignertype distribution defined by Claasen and Mecklenbrauker has become popular as a signal analysis tool. Moreover, it is commonly believed that ML detection of a discretetime chirp signal in white Gaussian noise can be done via the lineintegral transform of the WignerClaasenMecklenbrauker distribution. This belief is false and results in loss of performance. We derive a Wignertype distribution for discretetime signals whose lineintegral transform can be used for ML detection of discretetime chirp signals in white Gaussian noise. We provide simulated Receiver Operating Curves for the WignerClaasenMecklenbrauker distribution based method and the new MLequivalent method and demonstrate the suboptimality of the former. I.
Research Article Detection and Parameter Estimation of Multicomponent LFM Signal Based on the Cubic Phase Function
"... new algorithm for the detection and parameters estimation of LFM signal is presented in this paper. By the computation of the cubic phase function (CPF) of the signal, it is shown that the CPF is concentrated along the frequency rate law of the signal, and the peak of the CPF yields the estimate of ..."
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new algorithm for the detection and parameters estimation of LFM signal is presented in this paper. By the computation of the cubic phase function (CPF) of the signal, it is shown that the CPF is concentrated along the frequency rate law of the signal, and the peak of the CPF yields the estimate of the frequency rate. The initial frequency and amplitude can be obtained by the dechirp technique and fast Fourier transform. And for multicomponent signal, the CLEAN technique combined with the CPF is proposed to detect the weak components submerged by the stronger components. The statistical performance is analyzed and the simulation results are shown simultaneously. Copyright © 2008 Y. Wang and Y.C. Jiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
doi:10.1155/2009/727034 Research Article Adaptive Algorithm for ChirpRate Estimation
, 2009
"... Chirprate, as a second derivative of signal phase, is an important feature of nonstationary signals in numerous applications such as radar, sonar, and communications. In this paper, an adaptive algorithm for the chirprate estimation is proposed. It is based on the confidence intervals rule and the ..."
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Chirprate, as a second derivative of signal phase, is an important feature of nonstationary signals in numerous applications such as radar, sonar, and communications. In this paper, an adaptive algorithm for the chirprate estimation is proposed. It is based on the confidence intervals rule and the cubicphase function. The window width is adaptively selected to achieve good tradeoff between bias and variance of the chirprate estimate. The proposed algorithm is verified by simulations and the results show that it outperforms the standard algorithm with fixed window width. Copyright © 2009 Igor Djurović et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
Robust Sparse Component Analysis Based on a Generalized Hough Transform
, 2007
"... An algorithm called Hough SCA is presented for recovering the matrix A in x(t) = As(t), where x(t) isamultivariateobserved signal, possibly is of lower dimension than the unknown sources s(t). They are assumed to be sparse in the sense that at every time instant t, s(t) has fewer nonzero elements t ..."
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An algorithm called Hough SCA is presented for recovering the matrix A in x(t) = As(t), where x(t) isamultivariateobserved signal, possibly is of lower dimension than the unknown sources s(t). They are assumed to be sparse in the sense that at every time instant t, s(t) has fewer nonzero elements than the dimension of x(t). The presented algorithm performs a global search for hyperplane clusters within the mixture space by gathering possible hyperplane parameters within a Hough accumulator tensor. This renders the algorithm immune to the many local minima typically exhibited by the corresponding cost function. In contrast to previous approaches, Hough SCA is linear in the sample number and independent of the source dimension as well as robust against noise and outliers. Experiments demonstrate the flexibility of the proposed algorithm.
Open Access
"... Filtering in the joint time/chirprate domain for separation of quadratic and cubic phase chirp signals ..."
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Filtering in the joint time/chirprate domain for separation of quadratic and cubic phase chirp signals