A generalization of the Whittaker–Shannon interpolation formula for non-bandlimited signals

Reconstructing continuous signals from discrete samples is a fundamental task in interpolation theory. Under ideal assumptions, the classical Whittaker–Shannon interpolation formula guarantees perfect reconstruction for bandlimited signals sampled at the Nyquist rate. However, many real-world systems, particularly sampled-data systems, produce non-bandlimited signals whose intersample behavior is governed by the continuous-time dynamics encoded in the system model, making classical bandlimited reconstruction methods inappropriate. This paper presents a generalized interpolation framework that reconstructs continuous-time outputs from their samples using a model-induced kernel, thereby extending Shannon’s formula to a broader class of signals. The proposed method derives the interpolation kernel from the governing equations of the underlying system, enabling accurate reconstruction of intersample content. Numerical simulations and laboratory experiments on a permanent magnet synchronous machine (PMSM) validate the approach, demonstrating its effectiveness in reconstructing intersample behavior from output samples by leveraging model information.