A Take on Arbitrary Transient Electric Field Reconstruction Using Wavelet Decomposition Theory Coupled With Particle Swarm Optimization

Destructive and constructive interference of multiple time-shifted and amplitude-adjusted higher frequency signals (wavelet signals) is exploited in order to reproduce a desired signal at a given point in the far-field regime of radiating antennas. The number of individual wavelets is intentionally kept small in keeping with a realistic antenna array size, where each antenna would emit wavelets at conceivably very high power levels. Wavelet decomposition theory is coupled with particle swarm optimization to determine the necessary time shifts and amplitude adjustments of the wavelet signals. In this application, the reconstructed signal can be specified by a desired frequency or arbitrary shape. A pyramidal horn antenna array is used in the analysis of the far-field propagation of the wavelet signals due to its relatively large bandwidth and known analytical electric field solutions. It is found that when the wavelet signals are appropriately superpositioned and added in the far field, the desired signal may be reconstructed with the quality of reconstruction mostly governed by the intentionally low number of wavelets. The reconstructed signal is solely found on the centerline while the signal drastically changes off the centerline or at distances too close or too far from the antenna array.