Reducing the computational complexity of narrowband 2D fan filters using shaped 2D window functions

Two-dimensional (2D) discrete-domain FIR narrow fan filters may be used for the selective filtering of sampled broadband 2D plane waves on the basis of their directions of arrival (DOA). We show that the 2D region of support (ROS) of the unit impulse response h(n₁,n₂) of such filters may be reduced in size by using a shaped 2D window function, where the shape is determined by the angle and angular width of the fan. Relative to the widely used square-shaped window function, significant reductions in computational complexity are demonstrated using various shaped window functions. An approximately parabolically-bounded (PB) shaped 2D window function is shown to be especially effective. The method may be extended to 3D cone filters, for which the reduction in computational complexity is expected to be larger than for the 2D case.