Wavelet decomposition and reconstruction are utilized to synthesize a high power microwave (HPM) signal at a frequency below the frequency of the employed radiating sources. Employing a larger number (on the order of ten) of smaller sources that produce short radiating pulses combined with appropriate amplitude scaling and shifting of the individual pulses enables the generation of a single waveform of longer duration. We describe the mathematical approach to the wavelet synthesis and give examples. For instance, an array of 10 sources, each producing a 0.5 ns pulse can be adjusted to generate a sinusoidal wave with a period of approximately 2 ns. The results of low power experiments are discussed in detail to demonstrate the practical feasibility of the wavelet approach.