Interpolation-Free Mutilevel Plane Wave Transform

The plane wave transform (PWT) is a critical operation in computational electromagnetics. Accurate multilevel implementations of the PWT often rely on FFT-based interpolation and filtering operations when performing inter-level pattern aggregation and disaggregation. This presentation reports an alternative, explicitly sparse representation of the PWT. For a 2-D implementation, it is shown that the complexity of the resulting multilevel PWT is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O({N} \text{log}{N})$</tex>.