On the Compressibility of State Snapshots for String Systems
Chenyan Zhu, Sandip Roy · 2024
Sparse representation of the states of strings or cascades of dynamical systems is examined. Specifically, a notion of compressibility for string system states is introduced, which captures whether and to what extent the state can be expressed sparsely in a fixed basis. For a highly simplified string system model (made up of scalar, linear, discrete-time objects), compressibility in the Laplacian spectrum and Gramian spectrum bases is characterized analytically. The main result of this analysis is that the energy in the state snapshot is captured in a diminishing fraction of the basis vectors, as the string is made long. Simulations are used to illustrate the formal results, and demonstrate state recovery from sparse, randomly-located samples.