TY - JOUR
T1 - Accurate Interpolation of Amplitude-Only Frequency Domain Response Based on an Adaptive Cauchy Method
AU - Yang, Jie
AU - Sarkar, Tapan K.
N1 - Funding Information:
This work was supported in part by the National Natural Science Foundation of China (NSFC) under award no. 61372015, in part by the Research Fund for the Doctoral Program of Higher Education under award no. 20130042120023, and in part by the Fundamental Research Funds for the Central Universities in China under award no. N120204001.
Publisher Copyright:
© 2016 IEEE.
PY - 2016/3
Y1 - 2016/3
N2 - In this paper, a fast and accurate interpolation algorithm is proposed to reconstruct the high resolution amplitude only frequency domain response such as radar cross section and antenna radiation patterns from sparse and nonuniform samples based on the Cauchy method. For the Cauchy method, the amplitude only system frequency response is represented by a ratio of two polynomials, whose coefficients are estimated by using the conjunction of total least square (TLS) methodology, singular value decomposition (SVD) and conjugate gradient methods. Nonuniform sampling is implemented in Cauchy method such that any additional samples and any a priori information can be added to the existing sample set to continuously improve the interpolation result. In this proposed algorithm, the sample set is automatically adjusted according to the nature of the given data, so that the computational load is minimized by taking the least number of sample points while still maintaining high interpolation accuracy. Even though the Cauchy method can accurately interpolate the data containing both amplitude and phase, in this paper, the application is illustrated for the interpolation of amplitude only data, which may not be differentiable at all points.
AB - In this paper, a fast and accurate interpolation algorithm is proposed to reconstruct the high resolution amplitude only frequency domain response such as radar cross section and antenna radiation patterns from sparse and nonuniform samples based on the Cauchy method. For the Cauchy method, the amplitude only system frequency response is represented by a ratio of two polynomials, whose coefficients are estimated by using the conjunction of total least square (TLS) methodology, singular value decomposition (SVD) and conjugate gradient methods. Nonuniform sampling is implemented in Cauchy method such that any additional samples and any a priori information can be added to the existing sample set to continuously improve the interpolation result. In this proposed algorithm, the sample set is automatically adjusted according to the nature of the given data, so that the computational load is minimized by taking the least number of sample points while still maintaining high interpolation accuracy. Even though the Cauchy method can accurately interpolate the data containing both amplitude and phase, in this paper, the application is illustrated for the interpolation of amplitude only data, which may not be differentiable at all points.
KW - Adaptive interpolation
KW - antenna radiation pattern
KW - frequency response
KW - radar cross section
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U2 - 10.1109/TAP.2016.2518651
DO - 10.1109/TAP.2016.2518651
M3 - Article
AN - SCOPUS:84963752148
SN - 0018-926X
VL - 64
SP - 1005
EP - 1013
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 3
M1 - 7384447
ER -