Plate impulse response spatial interpolation with sub-Nyquist sampling

Impulse responses of vibrating plates are classically measured on a fine spatial grid satisfying the Shannon–Nyquist spatial sampling criterion, and interpolated between measurement points. For homogeneous and isotropic plates, this study proposed a more efficient sampling and interpolation process, inspired by the recent paradigm of compressed sensing. Remarkably, this method can accommodate any star-convex shape and unspecified boundary conditions. Here, impulse responses are first decomposed as sums of damped sinusoids, using the Simultaneous Orthogonal Matching Pursuit algorithm. Finally, modes are interpolated using a plane wave decomposition. As a beneficial side effect, these algorithms can also be used to obtain the dispersion curve of the plate with a limited number of measurements. Experimental results are given for three different plates of different shapes and boundary conditions, and compared to classical Shannon interpolation.

► Modal shapes of plates can be approximated by sums of plane waves.
► This model is used to interpolate impulse responses from few measurements.
► The number of measurements can be less than required by the Shannon-Nyquist sampling theorem.