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Is uniqueness lost for under-sampled continuous-time auto-regressive processes?.
| Content Provider | CiteSeerX |
|---|---|
| Author | Ward, John Paul Kirshner, Hagai Unser, Michael |
| Abstract | Abstract—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. Index Terms—Approximation theory, sampling theory, stochastic processes. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Uniqueness Lost Under-sampled Continuous-time Auto-regressive Process Sampled Process Originates Non-unique Continuous-time Ar Sampling Rate Constraint Alternative Description Key Aspect Lebesgue Measure Zero Uniqueness Problem Continuous-time Auto-regressive Process Index Term Approximation Theory Stochastic Process Uniform Grid Current Estimation Algorithm Kronecker Approximation Theorem Single Continuous-time Model Complex Plane |
| Content Type | Text |
