Is Uniqueness Lost for Under-Sampled Continuous-Time Auto-Regressive Processes?
J.P. Ward, H. Kirshner, M. Unser
IEEE Signal Processing Letters, vol. 19, no. 4, pp. 183-186, April 2012.
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.
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AUTHOR="Ward, J.P. and Kirshner, H. and Unser, M.",
TITLE="Is Uniqueness Lost for Under-Sampled Continuous-Time
Auto-Regressive Processes?",
JOURNAL="{IEEE} Signal Processing Letters",
YEAR="2012",
volume="19",
number="4",
pages="183--186",
month="April",
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