Large antenna sizes present a severe limitation in the generation of low frequency signals. To alleviate this issue, a series of high frequency sources (and thus, smaller antenna sizes) may be combined to produce a lower frequency output in the far-field. This reconstruction technique applies to signals of arbitrary shapes in addition to frequency lowering. Due to the large parameter space, wavelet decomposition theory is coupled with particle swarm optimization to define appropriate time shifts and amplitude adjustments to the high frequency sources (wavelets) in order to synthesize an output signal with the desired frequency or shape. Fifteen individual high frequency wavelets (f = 1 GHz) are utilized in this application to produce a final output signal in the far-field of 600 MHz the radiation of a single wavelet is simulated using a broadband Chebyshev TEM horn antenna in order to perform far-field constructive and destructive interference analysis of all 15 wavelet signals. Simulation of the TEM horn antenna shows reasonable wavelet signal fidelity with minimal reflections from the antenna aperture as the pulse is propagated to the far-field. Examination of the far-field electric field enables accurate temporal depiction of the reconstructed signal from the 15 pulsed sources at any given point in space. By adjusting the source array geometry, the location of the desired signal (determined by the particle swarm optimization) can be narrowed down to a single location. Overall, combining particle swarm optimization, wavelet decomposition theory, and electromagnetic wave propagation enables the accurate reconstruction of far-field temporal electric fields from the combination of 15 wavelet sources and verification of the desired signal location.