Using the matrix pencil method to estimate the parameters of a sum of complex exponentials

Sarkar, Tapan K.; Pereira, O.J.B. Almeida

doi:10.1109/74.370583

Cited by 1,030 publications

(542 citation statements)

References 38 publications

(12 reference statements)

Supporting

Mentioning

532

Contrasting

Unclassified

Order By: Relevance

“…Note that more advanced methods for computing the unknown frequencies were developed, such as matrix pencil methods. In [13,14] a relationship between the matrix pencil methods and several variants of the ESPRIT method [15,16] is derived showing comparable performance. Now we replace the steps 1 -5 of Algorithm 4.7 by the least squares ESPRIT method [17, p. 493].…”

Section: Nmmentioning

confidence: 99%

“…Clearly, we can choose the parameter L similarly as suggested in [14] based on the accuracy ε 2 as in Algorithm 4.7. Furthermore we would like to point out that in Algorithm 4.8 the right singular vectors of H related to the small singular values are discarded, otherwise the Algorithm 4.7 uses right singular vectors related to the small singular values in order to compute the roots of the corresponding polynomials.…”

Section: Form the Perturbed Rectangular Hankel Matrix (32)mentioning

confidence: 99%

See 1 more Smart Citation

Parameter estimation for exponential sums by approximate Prony method

2010

View full text Add to dashboard Cite

The recovery of signal parameters from noisy sampled data is a fundamental problem in digital signal processing. In this paper, we consider the following spectral analysis problem: Let f be a real-valued sum of complex exponentials. Determine all parameters of f , i.e., all different frequencies, all coefficients, and the number of exponentials from finitely many equispaced sampled data of f . This is a nonlinear inverse problem. In this paper, we present new results on an approximate Prony method (APM) which is based on [1]. In contrast to [1], we apply matrix perturbation theory such that we can describe the properties and the numerical behavior of the APM in detail. The number of sampled data acts as regularization parameter. The first part of APM estimates the frequencies and the second part solves an overdetermined linear Vandermonde-type system in a stable way. We compare the first part of APM also with the known ESPRIT method. The second part is related to the nonequispaced fast Fourier transform (NFFT). Numerical experiments show the performance of our method.

show abstract

Section: Nmmentioning

confidence: 99%

Section: Form the Perturbed Rectangular Hankel Matrix (32)mentioning

confidence: 99%

Parameter estimation for exponential sums by approximate Prony method

2010

View full text Add to dashboard Cite

show abstract

“…The interest for the characterization of targets led to the development of algorithms for finding resonance poles and their associated residues, using either the impulse response of targets in the time domain or their transfer function in the frequency domain [2,[9][10][11][12][13][14][15][16][17][18]. For our simulations, we can use any of existing methods of poles extraction.…”

Section: Resonances Poles Of Radar Targetsmentioning

confidence: 99%

Characterization of Perfectly Conducting Targets in Resonance Domain With Their Quality of Resonance

Chauveau¹,

Beaucoudrey²,

Saillard³

2007

PIER

View full text Add to dashboard Cite

Abstract-In resonance domain, the radar scattering response of any object can be modelled by natural poles of resonance with the formalism of the Singularity Expansion Method. The mapping of these poles in the complex plane gives useful information for the discrimination of a radar target, as its general shape, its characteristic dimension and its constitution. In this paper, we use an analogy with resonant circuits modelling to define the quality factor Q of each resonance. Therefore, we propose to characterize the resonance behavior of perfectly conducting targets with this quality factor Q and the natural pulsation of resonance ω 0 . Indeed, this new representation in {ω 0 ; Q} allows to better separate information than the usual mapping of natural poles of resonance in the complex plane. For perfectly conducting canonical and complex shape targets, we present results exhibiting advantages of these two parameters {ω 0 ; Q}.

show abstract

“…Sensitivity to input time or frequency samples have been handled by the modified LSProny [54] and TLS-Prony [55] methods, and other techniques based on the use of the singular value decomposition [56]. The Matrix Pencil Method (MPM) [7] has also been used for applications in low signal-tonoise ratio environments. Iterative search methods based on NewtonRaphson methods are also applied [57].…”

Section: The Common Sem Solutionmentioning

confidence: 99%

“…Singular value decomposition methods, such as the Matrix Pencil Method [7] have recently been used to minimize the effects of minor fluctuations (improve tolerance to noisy data) in excitation or field strength on the accurate solution of poles and residues. Many recent papers treat SEM as an abstract procedure for approximation of the response of objects to incident radiation, in certain cases referring to Model-Based Parameter Estimation (MBPE), an abstraction of SEM [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

A Common Theoretical Basis for Preconditioned Field Integral Equations and the Singularity Expansion Method

Fleming¹

2008

PIER M

View full text Add to dashboard Cite

Abstract-It is demonstrated that there is a common theoretical basis for the Singularity Expansion Method (SEM) and stabilized, preconditioned electric field and magnetic field integral equations (EFIE, MFIE) defining radiation and scattering from a closed perfect electric conductor in a homogeneous medium.An operator relation termed the Calderon preconditioner links the MFIE and EFIE, based on the fundamental Stratton-Chu integral representations for the problem geometry. This preconditioner is known to stabilize the ill-posed first kind EFIE, yielding the Modified EFIE (MEFIE). The same preconditioner has been applied to the weakly singular MFIE kernel, giving a Modified MFIE (MMFIE), the equation then being solved using the Fredholm determinant theory. Since this analytical integral theory is the foundation of the SEM, it follows that the Calderon preconditioner enables stabilized and common SEM representations to be defined for both the MEFIE and MMFIE.For a finite-sized object admitting only pole singularities, the solution of the preconditioned EFIE and MFIE is equivalent to the frequency-domain SEM solution. The common SEM representation differs only in the coupling coefficient terms. Coupling coefficients for the MFIE are known, however, explicit formulations for the EFIE, and the modified coupling coefficients for the MEFIE and MMFIE are new contributions.

show abstract

Using the matrix pencil method to estimate the parameters of a sum of complex exponentials

Cited by 1,030 publications

References 38 publications

Parameter estimation for exponential sums by approximate Prony method

Parameter estimation for exponential sums by approximate Prony method

Characterization of Perfectly Conducting Targets in Resonance Domain With Their Quality of Resonance

A Common Theoretical Basis for Preconditioned Field Integral Equations and the Singularity Expansion Method

Contact Info

Product

Resources

About