Signal approximation with Pascal's triangle and sampling

This brief explores the approximation properties of a unique basis expansion based on Pascal's triangle, which realizes a sampled-data driven approach between a continuous-time signal and its discrete-time representation. The roles of certain parameters, such as sampling time interval or model order, and signal characteristics, i.e., its curvature, on the approximation are investigated. Approximate errors in one and multiple-step predictions are analyzed. Furthermore, time-variant approximations under the thresholds of signal curvature are employed to narrow errors and provide flexibilities.