TY - JOUR

T1 - Theoretical formulation/development of signal sampling with an equal arc length using the frame theorem

AU - Xu, Chunying

AU - Chen, Jiawang

AU - Ge, Yongqiang

AU - Li, Miao

N1 - Funding Information:
This work was supported by the National Natural Science Foundation of China (Grant No. 42106205 and 41976055), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2019A1515110372 and 2021A1515011475), and STU Scientific Research Foundation for Talents (Grant No. NTF19034).
Publisher Copyright:
© 2022, The Author(s).

PY - 2022/12

Y1 - 2022/12

N2 - Nonuniform sampling with equal arc length intervals can be found in shape measurements with contact sensor arrays. In this study, the conditions of nonuniform spatial sampling with an equal arc length interval are derived from two frame theorems. First, for general nonuniform sampling, the condition is that the equal arc length interval of the sensors should be less than 14Ω. Second, for strictly increasing sampling (the sampling point set is strictly increasing), the condition is that the equal arc length interval of the sensors should be less than 12Ω. The Ω is the maximum frequency of the detected object. For the latter, if the sampling frequency is more than twice the sampling frequency required, the reconstruction error (RRMSE and MRE) is less than 5%. If the sampling frequency is more than 2.5 times, the reconstruction error is less than 3%. The simulation and the application test are carried out, and the results show that a sensor array with equal arc length interval can reconstruct the detected object with high accuracy.

AB - Nonuniform sampling with equal arc length intervals can be found in shape measurements with contact sensor arrays. In this study, the conditions of nonuniform spatial sampling with an equal arc length interval are derived from two frame theorems. First, for general nonuniform sampling, the condition is that the equal arc length interval of the sensors should be less than 14Ω. Second, for strictly increasing sampling (the sampling point set is strictly increasing), the condition is that the equal arc length interval of the sensors should be less than 12Ω. The Ω is the maximum frequency of the detected object. For the latter, if the sampling frequency is more than twice the sampling frequency required, the reconstruction error (RRMSE and MRE) is less than 5%. If the sampling frequency is more than 2.5 times, the reconstruction error is less than 3%. The simulation and the application test are carried out, and the results show that a sensor array with equal arc length interval can reconstruct the detected object with high accuracy.

KW - Equal arc length interval

KW - Frame theorem

KW - Nonuniform spatial sampling

KW - Reconstruction

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U2 - 10.1186/s13634-022-00888-x

DO - 10.1186/s13634-022-00888-x

M3 - Article

SN - 1687-6172

VL - 2022

SP - 1

EP - 18

JO - Eurasip Journal on Advances in Signal Processing

JF - Eurasip Journal on Advances in Signal Processing

IS - 1

M1 - 59

ER -