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

Abstract Nonuniform sampling with equal arc length intervals can be found in shape measurements contact sensor arrays. In this study, the conditions of nonuniform spatial an interval are derived from two frame theorems. First, for general sampling, condition is that sensors should less than $$\frac{1}{4\Omega }$$ 1 4 Ω . Second, strictly increasing (the point set increasing), $$\frac{1}{2\Omega 2 The $$\Omega$$ maximum frequency detected object. For latter, if more twice required, reconstruction error (RRMSE and MRE) 5%. If 2.5 times, 3%. simulation application test carried out, results show a array reconstruct object high accuracy.