Loading...
research article
Is Uniqueness Lost for Under-Sampled Continuous-Time Auto-Regressive Processes?
We consider the problem of sampling continuous-time auto-regressive processes on a uniform grid. We investigate whether a given sampled process originates from a single continuous-time model, and address this uniqueness problem by introducing an alternative description of poles in the complex plane. We then utilize Kronecker's approximation theorem and prove that the set of non-unique continuous-time AR(2) models has Lebesgue measure zero in this plane. This is a key aspect in current estimation algorithms that use sampled data, as it allows one to remove the sampling rate constraint that is imposed currently.
Type
research article
Web of Science ID
WOS:000300421100001
Authors
Publication date
2012
Publisher
Published in
Volume
19
Start page
183
End page
186
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
March 15, 2012
Use this identifier to reference this record