dWFS: Distributedwave Field Synthesis

In this paper we consider the problem of using a network of sensor and actuator nodes, to synthesize a given desired wave field, in a given medium we refer to mis problem as the distributed wave field synthesis problem (dubbed dWFS). We formulate this problem as one of minimization of a quadratic function, subject to linear (and very sparse) constraints. This formulation results from a finite-element approximation of the underlying wave equation, which constraints the values that a field and the source that induces that field can take. We present a complete solution for a 1D vibration, although our solution method cart be readily extended to any number of dimensions. Numerical simulations are included