Frequency independence property of radiation spatial filters

It is known that a time harmonic boundary normal velocity field of a radiating object immersed in an acoustic fluid can be decomposed into a (efficiently) radiating and a non (efficiently) radiating components, belonging to two orthogonal ‘‘radiating’’ and ‘‘evanescent’’ subspaces. Numerical results show the validity for a capped cylinder of the conjecture that the ‘‘radiating’’ subspace at a certain frequency f1 is a subspace of the radiating subspace at frequency f2≳f1. The implications are (a) from the output of a bank of spatial filters designed for the max frequency of operation the far field can be identified over the entire frequency band, and, perhaps more importantly, (b) if in an active control scheme the outputs of the filters are driven to zero, broadband cancellation of the radiating noise is achieved.