System identifiability for sparse and nonuniform samples via spectral analysis

The system identifiability for sparse and nonuniform measurements is addressed. For uniformly sampled data, spectral information is only available below the Nyquist rate. Hence, it is not necessarily “informative enough”, which is a prerequisite for system identifiability. Spectral analysis is carried out to reassess this issue. The result shows that nonuniform sampling pattern with some random distributions can keep alias-free and reproduce the spectrum from sparse samples, so that identifiability is still guaranteed. The model error bounds for aliased signal and finite data sets are also demonstrated.