Time and Frequency Bias in Extrapolating Wideband Responses of Resonant Structures

Frye, Joan M.; Martin, A.Q.

doi:10.1109/tap.2009.2033285

Cited by 3 publications

(29 citation statements)

References 14 publications

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“…CEM methods in time domain require lots of time steps to obtain a complete temporal response, while a broad-band solutions in frequency domain need to conduct computation at a large number of frequency points. In order to reduce the computational intensity of CEM, some researchers have proposed an extrapolation scheme [1][2][3][4][5][6][7][8] that the electromagnetic responses are extrapolated from early-time and low-frequency data by fitting a set of orthogonal functions and its Fourier transform. The missing late-time and high-frequency part is generated by the complementary information in both domains.…”

Section: Introductionmentioning

confidence: 99%

“…Since it is assumed that the conducting objects are excited by an approximately bandlimited incident electromagnetic wave, the temporal response is also an approximately band-limited function. However, the associated orthogonal polynomials used in [1][2][3][4][5][6][7][8] are not band-limited, which has a serious drawback that the extrapolation schemes are highly sensitive to noise in the known part of the electromagnetic response. For above reasons, an optimal choice of basis functions would be approximate prolate (AP) functions which are naturally band-limited and well suited for transient signals with compact support.…”

Section: Introductionmentioning

confidence: 99%

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Extrapolation of Transient Electromagnetic Response Using Approximate Prolate Series

Zhu¹

2015

PIER Letters

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A novel technique for extrapolation of transient response using early-time and low-frequency data is proposed in this paper. An improved extrapolation scheme using approximate prolate series is presented to obtain a transient electromagnetic response. The approximate prolate series, which has an approximately band-limited and sub-domain nature, is a better choice for extrapolating the timedomain electromagnetic response than orthogonal polynomials, such as Laguerre functions and Hermite functions. A novel regularization method based on truncated generalized SVD is also proposed to solve the ill-posed extrapolation problems, which make the extrapolation technique much less sensitive to noise in the known part of the response. Some numerical results are presented to illustrate the effectiveness and accuracy of the proposed method in extrapolation of transient electromagnetic problems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extrapolation of Transient Electromagnetic Response Using Approximate Prolate Series

Zhu¹

2015

PIER Letters

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…In [1][2][3][4], electromagnetic responses, such as the driving-point current of an antenna, are simultaneously extrapolated in time and frequency by fitting discrete values of the response evaluated at early time and low-frequency points. Early-time and low-frequency data are mutually complementary and together can provide all the information needed to characterize the complete response [1][2][3][4]. Determining a wideband response of a resonant structure with computational electromagnetic (CEM) methods can be burdensome; however, extrapolation can significantly reduce the computational load since the complete response is not determined exclusively in either domain [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…Early-time and low-frequency data are mutually complementary and together can provide all the information needed to characterize the complete response [1][2][3][4]. Determining a wideband response of a resonant structure with computational electromagnetic (CEM) methods can be burdensome; however, extrapolation can significantly reduce the computational load since the complete response is not determined exclusively in either domain [1,2].…”

Section: Introductionmentioning

confidence: 99%

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Wideband Extrapolation of Spatial Responses of Resonant Structures Using Early-Time and Low-Frequency Data

Frye

Martin

2013

Journal of Computational Methods in Physics

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An efficient procedure is presented to extrapolate a wideband electromagnetic response defined over an arbitrary spatial region using early-time and low-frequency data. The previous procedures presented in the literature are efficient for single-point extrapolation and can readily be applied to spatial regions but are terribly inefficient when a response is desired at many spatial locations. In this work, an optimized algorithm is presented to quickly extrapolate over a large number of spatial locations. The time and frequency behavior of the response is fitted by polynomials and pole terms, and the spatial variation is represented with spatially dependent polynomial coefficients and pole residues. A single set of poles, common to all spatial locations of interest, is shown to sufficiently describe the resonant behavior of response over the entire spatial region. A multisignal formulation of the matrix pencil method is applied to determine poles from early time data. Numerical examples are presented to demonstrate the procedure. Additionally, an automated approach to distinguish physical poles, which correspond to structural resonances, from nonphysical fitting poles is presented. The spatially dependent residues of physical pole terms, referred to here as modal residues, are shown to provide important insight into the resonant behavior of a structure.

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Extrapolation of Wideband Electromagnetic Response Using Sparse Representation

Zhao

Zhang

2012

IEEE Trans. Antennas Propagat.

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Time and Frequency Bias in Extrapolating Wideband Responses of Resonant Structures

Cited by 3 publications

References 14 publications

Extrapolation of Transient Electromagnetic Response Using Approximate Prolate Series

Extrapolation of Transient Electromagnetic Response Using Approximate Prolate Series

Wideband Extrapolation of Spatial Responses of Resonant Structures Using Early-Time and Low-Frequency Data

Extrapolation of Wideband Electromagnetic Response Using Sparse Representation

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