Title

Waveform Reconstruction for Recurrent Non-uniform Discrete-time Sampling Scheme: Discussion of Its Instability

Published In

2016 IEEE International Instrumentation and Measurement Technology Conference Proceedings

Document Type

Citation

Publication Date

2016

Abstract

The main purpose of this paper is to analyze the instability in waveform reconstruction from non-uniformly sampled signals generated by recurrent non-uniform discrete-time sampling scheme. From the applied equation, the matrix of conversion, [A], associates the uniformly sampled signals to non-uniformly sampled ones, and plays a key role in the reconstruction. To recover the uniformly sampled signals, we need to compute the inversion of [A], [A]-1. Although [A]-1 is known to be numerically unstable in some occasions, the fundamental reason and premise for this instability have not been discussed. Thus, by obtaining the closed form of det[A], this paper shows that the root cause of the instability of [A]-1 is related to the singularity of [A], which has det[A] = 0 resulting from specific patterns of timing offsets in the recurrent nonuniform discrete-time sampling scheme. Numerical results confirm the analysis.

DOI

10.1109/I2MTC.2016.7520364

Persistent Identifier

https://archives.pdx.edu/ds/psu/25924

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